The comments, made three days before critical primaries in several states, including Florida and Ohio, represent an escalation in Rubio's rhetoric, and follow a Republican debate earlier this month
in which Rubio vowed to back Trump were he to become the GOP's standard-bearer.
"I still, at this moment, continue to intend to support the Republican nominee," Rubio told reporters in Largo, Florida. "But (it's) getting harder every day."
Rubio added, "I believe Donald Trump as our nominee is going to shatter and fracture the Republican Party and the conservative movement. I think it's already having that function."
The Florida Republican returned to a theme he advanced during CNN's GOP debate Thursday -- that words have consequences -- as he weighed in on the protests at Trump's Friday rally in Chicago. The Trump campaign postponed the event amid security concerns and scuffles among protesters and supporters.
"I think we also have to look at the rhetoric coming from the front-runner in the presidential campaign," Rubio said. "Someone who's basically encouraged people in the audience to rough up anyone who stands up and says something he doesn't like."
Rubio said if the anger from voters continues, the country will "continue to be ripped apart at the seams."
"There's a broader issue in our political culture in this country. And this is what happens when a leading presidential candidate goes around feeding into a narrative of anger and bitterness and frustration," Rubio said, adding later, "I'm sad for this country."
On Saturday afternoon, Trump resumed to calling Rubio a "choker," an insult he's used before on the Florida senator.
"What is he? He's a choke artist who never goes to vote," Trump said at a rally in Cleveland, referencing Rubio's attendance rate in the Senate. "Who the hell wants him to represent you? Who? So I think Marco's got a lot of problems."
In an interview with The New York Times
that was published on Saturday, Rubio likened Trump to a third-world dictator.
"Most countries around the world that are failures are because they deposit their hopes in a person, a strong leader who comes forward and says 'Put me in power. And I will make the country better,'" Rubio told the paper.
"That's exactly what he's doing," Rubio continued. "The rhetoric reminds me of third-world strongmen."
In an interview after the rally was postponed on Friday night, CNN's Don Lemon asked Trump if he had any regrets about the charged rhetoric at his rallies.
"I don't have regrets," Trump said. "These were very, very bad protesters. These were bad dudes. They were rough, tough guys."
According to the latest CNN poll of polls
, Trump holds a substantial lead over Rubio in Florida, 40% to 26%, respectively. Texas Sen. Ted Cruz has 18% of the vote and Ohio Gov. John Kasich is at 8%.