Sen. Marco Rubio (R-Fla.) walks out of Oxford Exchange during a campaign stop in Tampa on Saturday. (Andrew Harrer/Bloomberg News)

TAMPA -- Sen. Marco Rubio (R-Fla.) said Saturday that "There's no doubt" President Obama has helped stoke the caustic rhetoric and violence displayed at recent political rallies held by Republican presidential front-runner Donald Trump.

Earlier Saturday, Rubio lashed out at his rival Trump for failing to condemn violent protests at his recent public events and lamented that the increasingly nasty nature of American politics "is now bleeding over into the broader culture." But he also faulted Obama, saying the president had contributed to the coarsening political debate.

Republican presidential candidate Marco Rubio on Saturday, March 12 faulted Republican front-runner Donald Trump for not condemning violence that has occurred at Trump rallies. (Reuters)

Asked in an interview to give a specific example of how Obama has divided the country, Rubio cited an April 2011 speech used to criticize a budget proposal written by then-House Budget Chairman Paul Ryan (R-Wis.). With Ryan sitting in the audience, Obama said that the GOP's budgeting vision "is less about reducing the deficit than it is about changing the basic social compact in America."

"He basically said, 'If you agree with Paul Ryan’s budget, you don’t care about the disabled, you don’t care about the elderly, you don’t care about the poor,'" Rubio recalled. "There’s been numerous instances where he basically implies that if you don’t care with his gun control agenda than you didn’t care about the kids who died at Sandy Hook. Time and again he’s done that. There’s no doubt that he’s been a contributor to this."

"I think all of us in American public office need to take a step back and examine ourselves and say, 'Have we contributed to this culture that’s emerged where you literally have a country where people hate each other?'" Rubio said. "We have an America where Americans are starting to hate each other. I mean, we can have policy disagreements, and they should be vibrant, but there’s got to be a limit to it. Otherwise we can’t function as a country."

Referring to the 2011 speech, Obama told The Washington Post's Bob Woodward that he didn't know Ryan was going to attend the event at George Washington University and said that in retrospect, it was "a mistake" to criticize the future speaker and his budget plans with him in the audience.

On Friday, Obama said he was unsurprised by Trump's rise.

President Obama took aim at Donald Trump and the Republican party at a fundraiser in Austin, Tex., where he described the Republican campaign as ranging from "school yard" taunts to scenes from "the home shopping network." (Reuters)

“How can you be shocked?” the president asked during a speech at a Democratic National Committee event at  Texas’s Austin Music Hall. “This is the guy, remember, who was sure that I was born in Kenya — who just wouldn’t let it go. And all this same Republican establishment, they weren’t saying nothing. As long as it was directed at me, they were fine with it. They thought it was a hoot, wanted to get his endorsement. And then now, suddenly, we’re shocked that there’s gambling going on in this establishment.”

In the interview in Tampa, Rubio also said that other Republicans, including rival candidate Sen. Ted Cruz (R-Tex.) are "going to have to answer why they enabled [Trump] for almost a year."

"Ted Cruz, up until two months ago, was still bear-hugging Donald Trump and refusing to condemn any of the things he said," Rubio said. "I recall very clearly that when he said John McCain was a loser because he had been captured that I condemned him, as did others. It didn’t seem to matter. The other night at the debate stage when I asked about his comments about all Muslims hating America, I condemned him."

The Cruz campaign on Saturday night disputed Rubio's characterization of how the Texan has campaigned against Trump. A spokeswoman noted that Cruz raised concerns with Trump's proposals in the weeks before the Iowa caucus when the two men were trading places atop polls there.

Rubio said he thinks Trump "has figured out a formula, and that is, he can say outrageous things and he will get a lot of coverage for it."

Rubio added: "And it is part of a game he’s playing where he is tapping into peoples’ anger, and instead of saying, ‘I know you’re angry, you have a right to be angry, here’s how we’re going to fix it,’ he says to them, ‘I know you’re angry, you should be even angrier, here’s who we should be angry at, give me power so we can go after them.’ And it’s leading us to this boiling point we’ve now reached."

Earlier Saturday, Rubio grew visibly frustrated and his voice cracked with emotion when asked by reporters whether he could still support Trump as the GOP presidential nominee.

“I still at this moment continue to intend to support the Republican nominee, but it’s getting harder every day," he said.

Asked to reflect on the rise of Trump, Rubio said in the interview that it wasn't until after the businessman's victories in New Hampshire and South Carolina that he realized how the crowded GOP field might allow Trump to win the GOP nomination despite widespread opposition to his candidacy.

"I think as time went on and outrageous statements which normally disqualify someone for office didn’t seem to, everybody grew concerned," he said. "But you still hold out the hope that gravity would set in and that this is still a country where dignity and appropriate discourse was a pre-qualification for aspiring to the highest office in the land."

"After the results in New Hampshire and South Carolina," he said, "everyone started to wake up to the reality that the majority of Republicans don’t want Donald Trump to be their nominee. But all those people are divided up among five, six, seven names. And if this pattern continues, he could very well be the nominee. And it’s going to be very disruptive to the political process." he said.

Rubio spoke with The Washington Post on Saturday aboard his campaign bus parked outside the Oxford Exchange, a posh downtown Tampa store and restaurant. The stop came amid a whirlwind tour of the region that included an early morning rally in Largo and stops at diners and barbecue restaurants before an evening event in Pensacola. On Sunday Rubio is scheduled to visit The Villages, a sprawling retirement community north of Orlando, before visiting his campaign office in Orlando. By Monday night, he is expected to be home in Miami, where close political supporters are working this weekend to ensure that supporters vote early or plan to show up at the polls on Tuesday.

One prominent Florida Republican not helping Rubio this weekend is former Florida governor Jeb Bush, who ended his presidential bid last month. Bush met privately this week with Rubio, Cruz and Ohio Gov. John Kasich, but has no plans to make an endorsement before Tuesday's primary.

Rubio said he wasn't surprised. "We would have loved to have his endorsement, but I respect the fact that he’s not involved. At the end of the day, people make decisions like that all the time. It’s not a big deal," he said.

In seeking the presidency, Rubio declined to run for reelection to the U.S. Senate. No matter what happens with his presidential campaign in the coming days, he does not plan to resign the position before his term ends in January.

"I ran and got elected for a six-year term, and I’m going to finish the six-year term," he said. "There will be a new senator. There’s no sense in not fulfilling that term."