Republican presidential candidate Marco Rubio announced he was suspending his campaign as he took home no wins over this three rivals in five primaries: Florida, Illinois, Ohio, Missouri and North Carolina. (Sarah Parnass/The Washington Post)

The Democratic party moved a lot closer to choosing its nominee on Tuesday night. The Republican party moved a little closer to chaos.

Former secretary of state Hillary Clinton has won at least four of the five states where Democrats voted on Tuesday, with victories in Florida, Illinois, Ohio and North Carolina. The race in Missouri against Sen. Bernie Sanders (Vt.) remains too close to call. Clinton’s staff said they expected to increase their lead in the race for Democratic convention delegates by about 300 — requiring Sanders to stage a near-miraculous comeback in the coming states.

“We are moving closer to securing the Democratic party nomination and winning this election in November,” Clinton told supporters in West Palm Beach, Fla. Sounding hoarse, she seemed to be offering an olive branch to Sanders — who, so far, has shown little inclination to get out of a race that has given him an unprecedented national following. “I want to congratulate Senator Sanders for the vigorous campaign he’s waging,” Clinton said, giving it a try anyway. She has now won 15 states, as compared with nine wins for Sanders.

Tracking the race to the Democratic nomination

On the Republican side, GOP front-runner Donald Trump won a key contest in Florida — a lopsided victory on the home turf of rival Sen. Marco Rubio, which caused Rubio to declare he was suspending his campaign. That brought Trump all of Florida’s 99 Republican delegates, the biggest prize awarded in any state so far. Trump has also been projected as the winner in Illinois and North Carolina, two states with 141 delegates between them. But, because those are not “winner-take-all” states, Trump will likely have to split some of those 141 with other candidates. The GOP race in Missouri remains too close to call.

But Trump was denied a victory in another key winner-take-all state, Ohio, which was won by its own sitting governor, John Kasich. That victory doesn’t make Kasich a likely nominee: he has now won a grand total of one state. But, without Ohio’s 66 delegates, Trump now faces a difficult path to reach the majority of delegates he needs to avoid a “contested” GOP convention, in which no candidate enters with a majority of delegates locked up. In that chaotic situation — not seen in the GOP since 1976 — delegates could choose one of the candidates who ran, or someone else entirely. If their choice is not Trump, the party may have to face strong anger from his supporters, or even a third-party candidacy from Trump himself.

Trump spoke to supporters at his Mar-a-Lago club in Palm Beach, Fla., where he savored his victory over Rubio in Florida, despite a barrage of anti-Trump advertising. “Nobody has ever — ever, in the history of politics — received the kind of negative advertising that I have…vicious, horrible,” Trump said. But then, he said: “You explain it to me, because I can’t: my numbers went up.” He told supporters that he’d seen anti-Trump commercials during a broadcast of a golf tournament from Trump’s own club, and tried to distract attendees at the tournament from watching.

Trump repeated his promise to bring the Republican party together: “We have to bring our party together. We have to bring it together. We have something happening that actually makes the Republican party probably the biggest political story anywhere in the world.”

But he also, more than before, seemed to show signs of fatigue at the long grind of a campaign. Trump spoke of missing his youngest son, Baron, while he’s been out on the trail: “Baron. I never see my Baron,” Trump said. “He said, ‘When are you going to come home, Daddy? When are you coming home?’”

Trump’s top rival, in terms of delegates, is Sen. Ted Cruz (Tex.) — who has won no states so far, though he is running neck-and-neck with Trump in returns from Missouri. Before the outcome in Missouri was known, Cruz spoke to supporters in Houston, and essentially declared that Kasich — even on his best night of the campaign — would be a non-factor from here on out.

Tracking the race to the Republican nomination

“Only two campaigns have a plausible path to the nomination, ours and Donald Trump’s,” Cruz said. “Nobody else has any mathematical possibility whatsoever.” He praised Rubio at length, trying to win over Rubio’s supporters — and the “#nevertrump” crowd that had coalesced around Rubio. “We welcome you to our teams, we welcome you with open and welcoming arms,” Cruz said. That, in itself, was an amazing moment and a sign of how Trump has reshaped the Republican landscape this year.

A year ago, the idea that Cruz — the despised figure who led Republicans into an ill-fated effort to stop “Obamacare” and triggered a government shutdown instead — might be the best choice for the GOP establishment would have been too strange to be funny.

Kasich’s win in Ohio was celebrated by GOP operatives who launched a last-ditch campaign to thwart Trump’s march to the nomination.

“You’re not the nominee until you get 1,237 delegates, and I don’t see how Trump gets there,” said Katie Packer, the strategist helping lead Our Principles PAC, which has spent nearly $13 million on a barrage of hard-hitting ads attacking the billionaire real estate developer. “Our goal was always to deprive him of Ohio and Florida, and the fact that we got halfway, we consider a win for the American people and the Republican party and certainly us.”

Kasich has largely abstained from attacking Trump so far, but on Tuesday night – with the race narrowing, and his position improving – Kasich took a brief swipe at the front-runner. “I will not take the low road to the highest office in the land,” Kasich said. He took a remarkably different tone than the bombastic front-runner, who focuses on international trade and business deals. Kasich told his audience to make the world better in smaller ways, working harder at their jobs, and being kind to neighbors. At times, he did not seem to be speaking about a political campaign at all.

“We’re all part of a giant mosaic. A snapshot in time. All of us here,” Kasich said, saying that every person in the audience had a purpose from God. “Our job…is to dig down and understand that purpose, and never underestimate our ability to change the world in which we live.”

Rubio, a first-term senator, had launched his campaign with a message of youth and optimism — but was unable to escape his support for a 2013 effort at immigration reform, which many conservatives believed was too lenient on undocumented immigrants. And he was unable to escape Trump, who hectored him as “Little Marco,” a tool of big donors.

“After tonight, it is clear that — while we are on the right side — this year we will not be on the winning side,” Rubio said on Tuesday.

Rubio eventually fired back, trying to fight on Trump’s level with insults about the front-runner’s tan and his fingers. He also called Trump a “con artist” for his involvement in a “university” that many students said defrauded them. But Rubio undercut his own message by saying that he would still vote for Trump, were he the nominee.

That odd, mismatched strategy seemed to turn off voters: his poll numbers declined sharply. He won just one state, Minnesota, along with Puerto Rico and the District of Columbia. Rubio, oddly, mocked the District of Columbia by name in his speech.

“There’s nothing more you could have done,” Rubio said, speaking in the concourse of a Florida arena – he had rented the whole thing, but the crowd was so small that he only needed a hallway. “America’s in the middle of a real political storm. A real tsunami. And we should have seen this coming.”

Even in defeat, however, Rubio could not escape Trump. A heckler shouted out “Trump for President!” The crowd booed, but Rubio shushed them. “Don’t worry, he won’t get beat up at our event,” he said, referring to alleged assaults of protesters at Trump events.

In early exit polls reported by ABC News, Democratic primary voters had a split view of the two candidates: they tended to see Clinton as far more electable — but see Sanders as more honest. By a roughly 2 to 1 margin, Democratic voters said Clinton had a better chance than Sanders of beating Trump in a general election matchup across Ohio, North Carolina, Florida, Illinois and Missouri.

But roughly 8 in 10 said Sanders was honest and trustworthy, compared with about 6 in 10 for Clinton. Sanders has dominated among honesty-focused voters all year while Clinton has won those focused on electability by a wide margin.

According to those same early exit polls reported, large majorities of Democrats in Tuesday’s primaries would be satisfied with either Clinton or Sanders winning the Democratic nomination. At least 7 in 10 voters across primary voting states would be satisfied with each candidate becoming the party’s nominee, with slightly more satisfied with Clinton than Sanders.

Among Republican primary voters, by contrast, preliminary exit polls showed unusual hesitancy about the prospect of Trump as the nominee. Across all of Tuesday’s states, a little more than half of GOP voters said they would be satisfied with Trump as the Republican nominee against Clinton, according to early exit polls from ABC News.

Just under 4 in 10 Republican voters across Tuesday’s contests said they would consider a third-party candidate if Trump and Clinton were the nominees. Looking specifically at non-Trump supporters, ABC reported 6 in 10 would consider backing a third-party candidate if Trump became the party’s nominee.

Separately, it was clear from exit polls that the majority of Tuesday’s GOP voters supported Trump’s proposal temporarily to ban foreign Muslims from entering the United States. In all, 66 percent agreed with that idea, according to exit polls reported by ABC News.

Trump scored an early win Tuesday morning, swamping the tiny vote in a Republican caucus held in the Northern Mariana Islands, according to a tweet from the executive director of the GOP in the U.S. territory.

The win earned Trump nine delegates, only a tiny sliver of the 367 delegates at stake Tuesday. But should the chaotic Republican race lead to a contested national convention in July, the win could prove important because of arcane party rules that require candidates to have won a majority of delegates in at least eight states or territories. The win was Trump’s eighth of the nominating season.

Voting ran relatively smoothly across the country, although a frightening incident interrupted one Cleveland voting location, where police said a poll worker was arrested after pulling a gun during a verbal dispute with fellow workers.

A spokeswoman for the Cleveland Police Department said Alan Bethea, 45, faced multiple charges. Police say he pulled a .380 handgun from his backpack during the argument. No one was injured.

Ahead of Tuesday’s vote, Missouri officials had estimated 34.1 percent of voters would take part in the primary, nearing 2008’s record turnout of 36 percent. News reports in other parts of the country also reported lines in hotly contested races.

In North Carolina, where a controversial new voter identification law was in use for the first time, voting rights advocates were on alert for problems. A spokeswoman for the North Carolina State Board of Elections said late in the day that primaries were running smoothly.

In Ohio, some voters appreciated the job Kasich has done as governor.

“He’s done a great job for Ohio,” said Lauri Gillet, 42, a civil engineer who voted for Kasich in Westerville, the governor’s home town. “He’s the best of both worlds, from a business standpoint and a politics standpoint. And Ohio’s doing great. There’s been a ton of growth in the oil and gas industry.”

Hundreds of thousands of ballots were already cast in early voting in Florida. Turnout was light in the early morning at a polling place near the airport in Miami. But the voters who showed up sounded passionate about their choices.

Luis Joaquin Alonso, 79, said he voted for Trump, citing concerns about the deficit and the desire for someone to take on the political establishment.

“I love this country,” he said, adding that Trump does, too, and that’s why he is running.

“This guy has got plenty of money. He doesn’t need [more] money,” Alonso said.

Florida’s primary is closed, meaning that independents, who have sided with Sanders in large numbers in other states, could not participate. The state is also home to large numbers of seniors, who have gravitated far more heavily toward Clinton elsewhere.

In Miami, Luis Caldera, 61, said he voted for Clinton. He called her “the best option” and said her experience and his familiarity with her career set her apart.

In Youngstown, Ohio, Dave Williams, 52, cast a ballot for Sanders, deeming the Vermont senator better for working people.

“I lost my house when the stock market crashed. That was before the government was doing anything to keep people in their homes. And I’ve gone from a house since then to an apartment,” said Williams, a member of cement finishers local 179. “I’m an angry voter, how ’bout that? I’m angry about the way the country is working for the blue-collar worker. Hillary gets a big, fat zero on that.”

While out for breakfast Tuesday morning in downtown Chicago, Sanders predicted he could have a good night if larger numbers of voters take part in the contests — setting up a long nomination battle in states that are even friendlier to his campaign.

“I think that if there is a large voter turnout, we are going to do just great here in Illinois, in Missouri, Ohio, and hopefully North Carolina and Florida,” Sanders said during a stop at Lou Mitchell’s, a Chicago institution. “In the states that are coming down the pike, we have great opportunities to win many of them, so we are feeling really good.”

Sanders was accompanied by Cook County Commissioner Jesus “Chuy” Garcia, who ran unsuccessfully for mayor against Rahm Emanuel last year. Part of Sanders’s strategy in Illinois has been mobilizing those disappointed with the tenure of Emanuel, a Clinton ally whose approval ratings have dropped to all-time lows.

In North Carolina, Clinton campaigned at a polling place in Southeast Raleigh Magnet High School around midday on Tuesday, greeting supporters with hugs and selfies.

She warned that her supporters might see public polling that shows her with leads in many of the states voting Tuesday and conclude that they don’t need to vote, which her campaign believes might have contributed to her unexpected loss to Sanders in Michigan last week.

“Sometimes the reporting of polls, some might say: well, my candidate is doing so well, I don’t need to come out,” Clinton said. “But everybody should come out. There’s so much at stake in this election.”

Clinton has been eager to pivot her campaign to confront Trump more directly. But asked Tuesday if she was concerned that a protracted primary fight with Sanders would impede Democrats’ ability to wage a general-election fight against the GOP nominee, she declined to encourage Sanders to leave the race.

“He has a right to run his campaign in any way that he chooses, and I’m proud of the campaign we’ve run,” Clinton said.

Trump’s rhetoric drove some voters Clinton’s way in the Democratic contest. Tonya Massenburg, 53, voted for Clinton in Raleigh because she is primarily concerned about “violence” and “racism” in the country right now — and less concerned about Sanders, about whom she said she knows very little.

“I just hope that North Carolina pulled through for Hillary Clinton,” she said. “Because of the way this country is headed, it’s not very good.”

Also Tuesday, Clinton announced that she has been endorsed by the mother of Michael Brown, the teenager whose 2014 shooting by police in Ferguson, Mo., brought more attention to officer-involved slayings of unarmed black men.

The endorsement came as Clinton has appeared to lose ground to Sanders in Missouri, with the most recent poll showing an effective tie.

“When I lost my son, I lost my world. ‘Big Mike’ was a big boy, but he was my baby boy, my only child, and his life was brutally taken from me,” Lezley McSpadden wrote in her endorsement statement.

“This election season, we are at battle for the soul of our nation,” McSpadden said. “If we want to continue to build on the progress made by our country, we need a president who is ready to lead — and I trust Hillary Clinton.”

McSpadden was among a group of African-American mothers who met privately with Clinton last year, and Clinton has made the mothers’ stories a regular part of her political speeches, as she talks about the need for criminal justice reform and better gun control.

Helderman and Fahrenthold reported from Washington. Sean Sullivan and Ed O’Keefe in Miami, David Weigel in Youngstown, John Wagner in Chicago, Abby Phillip in Raleigh, and Scott Clement, Anne Gearan and Matea Gold in Washington also contributed.