Democratic front-runner Hillary Clinton and her opponent, Bernie Sanders, spoke about the challenges going forward after primary voters took to the polls in five states on March 15. (Sarah Parnass/The Washington Post)

Hillary Clinton won at least four of five primaries on Tuesday, pushing her closer to the Democratic presidential nomination as her considerably weakened rival Bernie Sanders vowed to press on with his insurgent campaign.

Clinton won big in Florida, North Carolina and Ohio, while claiming a narrower victory in Illinois. Missouri remained too close to call. Sanders’s campaign had hoped his raw message of economic justice would prevail in the industrial heartland.

But with her victories, Clinton was on track to collect a large share of the more than 1,000 delegates she still needed to lock up the contest. Sanders ended the day further behind in the delegate count — and needing to win a slew of upcoming states by improbably large margins.

“We are moving closer to securing the Democratic Party nomination and winning this election in November,” Clinton said at her victory party here Tuesday. As if to prove the point, she quickly pivoted to the Republican front-runner, Donald Trump.

“Our next president has to be ready to face three big tasks: First, can you make positive differences in people’s lives? Second, can you keep us safe? Third, can you bring our country together again?”

Clinton’s indictment of Trump’s policy positions sounded like a preview of arguments to come.

“When we hear a candidate for president call for the rounding up of 12 million immigrants, banning all Muslims from entering the United States, when he embraces torture, that doesn’t make him strong, it makes him wrong,” Clinton said.

Clinton has been eager to refocus her campaign to confront Trump more directly. But asked Tuesday if she was concerned that a protracted primary fight with Sanders would hobble Democrats ahead of the contest against a Republican nominee, she declined to encourage Sanders to leave the race.

Her campaign emailed a fundraising pitch Tuesday evening warning of the dangers of a Trump presidency and of complacency among Democrats.

“Tonight, Donald Trump could become the presumptive Republican nominee for president,” the donation request began. Too many Republicans tried to ignore him until it was too late, it said.

“It’d be easy for us Democrats to do the same thing now — Trump is so offensive, so vulgar, so self-evidently awful. You could look at him and think, ‘there’s no way he’ll ever get elected,’ and then just wish him away. But we can’t.”

Sanders held a rally before about 7,000 people in Phoenix on Tuesday night, a week ahead of Arizona’s primary.

Tracking the race to the Democratic nomination

He said his campaign had “defied all expectations” but made no mention of the three states that had already been called in Clinton’s favor.

“What excites me so much as I go around the country is to see the incredible energy of people who love this country but know we can do so much better,” Sanders said to loud screams.

In a statement several hours later, Sanders vowed to fight on, saying: “With more than half the delegates yet to be chosen and a calendar that favors us in the weeks and months to come, we remain confident that our campaign is on a path to win the nomination.”

Some of his die-hard supporters expressed hope that he could still pull out the nomination.

“I still think the revolution is coming,” said James Homan, 55, a sound engineer for rock musicians, who has homes in Illinois and Arizona.

Homan expressed frustration that, as he saw it, “the fix was in” for Clinton among Democratic Party leaders, but he said he could see paths for Sanders to prevail, including the possibility of more fallout from the FBI investigation into Clinton’s use of a private email server while she was secretary of state.

Democratic primary voters were split on the candidates’ key attributes, with Clinton seen as more electable and Sanders as more honest, according to preliminary exit polls reported by ABC News.

By roughly 2 to 1, voters across Ohio, North Carolina, Florida, Illinois and Missouri said Clinton had a better chance than Sanders of beating Trump in a general-election matchup. But roughly 8 in 10 said Sanders was honest and trustworthy, compared with about 6 in 10 who felt that way about Clinton. Sanders has dominated among honesty-focused voters all year, while Clinton has won by a wide margin those who care more about electability.

Sanders, an independent senator from Vermont, had scored an upset victory last week against Clinton in Michigan and saw Tuesday’s contests as a chance to pull off more come-from-behind wins in states where voters feel damaged by globalization.

Repeating his playbook from Michigan, Sanders hit Clinton hard on her past support for “disastrous” trade deals, starting with the North American Free Trade Agreement when her husband was in the White House.

After Clinton’s loss in Michigan called her economic message into question, her campaign moved to retool her stance on trade by strengthening her opposition to the Trans-Pacific Partnership and emphasizing support for manufacturing in her jobs plan. In Ohio, Clinton took specific aim at elements of the pending trade package seen as harmful to the auto and steel industries.

Just over half of Ohio Democratic primary voters said free trade takes away U.S. jobs, according to the early exit polls. In Michigan, Sanders won among voters with that view by double digits. The anti-trade cohort was slightly larger in Michigan (57 percent) than in most states voting Tuesday, with less than half of Democrats in Illinois, Missouri and North Carolina saying trade costs U.S. jobs.

In Youngstown, Ohio, Dave Williams, 52, cast a ballot for Sanders.

“I lost my house when the stock market crashed,” said Williams, a member of the local cement finishers union. “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.”

In Missouri, Sanders aides were optimistic in part because much of the state closely resembles Kansas, where the senator easily defeated Clinton in the Democratic caucuses early this month. It’s worth noting, however, that Missouri was the smallest of the Democratic delegate prizes Tuesday.

Before the polls closed in Missouri, Clinton’s campaign announced that she had 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.

Multiple polls in the days leading up to Tuesday’s contests showed Sanders closing in on Clinton in the three states in the industrial Midwest.

In Chicago, where Clinton spent her childhood, Sanders sought to leverage support from voters disenchanted with the tenure of the city’s embattled Democratic mayor, Rahm Emanuel, a Clinton ally. Emanuel’s approval ratings have dropped to all-time lows amid controversies over a police shooting and school closings, and his popularity with African American voters has taken an especially big hit.

In the closing days of the race, Sanders blasted Emanuel’s decision to close schools in predominantly black and Latino neighborhoods, and Sanders ran television ads featuring some of the mayor’s critics.

And Tuesday, Sanders had breakfast with Cook County Commissioner Jesús “Chuy” García, who ran unsuccessfully for mayor against Emanuel in the Democratic primary last year.

Clinton’s lead in Florida was never in doubt, and she ended up capturing almost the same number of votes as the Republican winner, Trump — perhaps a preview of how competitive the state will be in November.

Florida posed several challenges for Sanders. It held a closed primary, meaning independent voters, who have propelled him to victory in other states, were not allowed to participate. The state’s voting population also includes a large number of older voters, who have sided with Clinton in previous contests.

Sanders’s aides have argued that the back half of the nominating calendar is more favorable to him, with several potential victories in the West and no contests remaining in the Deep South, which has been Clinton’s strongest region by far.

Sanders thinks he is well-positioned in all three states with contests next Tuesday: Arizona, Idaho and Utah. His decision to spend election night in Arizona signaled his intention to vigorously contest that state in the coming week.

Scott Clement contributed to this report.