David M Jackson

USA TODAY

Donald Trump rejected responsibility Sunday for violence at his rallies and suggested his backers may retaliate by protesting Bernie Sanders events.

"Many of these people come from Bernie," Trump said on CBS' Face The Nation when asked about what he called "professional disrupters" who are attending his events.

Trump was more explicit in a Sunday tweet: "Bernie Sanders is lying when he says his disruptors aren't told to go to my events. Be careful Bernie, or my supporters will go to yours!"

Sanders, appearing on CNN's State of the Union, said Trump is the one creating a toxic atmosphere; the Democratic candidate said his campaign has had nothing to do with protests at Trump rallies, and that the Republican candidate is simply making things up, again.

"This man cannot stop lying about anything," Sanders said.

Trump did an array of Sunday show two days after canceling a rally in Chicago because of violence between supporters and critics.

Republican rivals say the violence is a natural outgrowth of Trump's rhetoric, such as statements he would like to punch a protester in the face, that some protesters could be taken out on stretchers, and that he would pay the legal fees of supporters who strike back. Last week, a supporter at a rally in North Carolina punched a protester in the face as police escorted him out.

Texas Sen. Ted Cruz, who is chasing Trump in the fight for delegates, told NBC's Meet The Press that it's wrong for protesters to try and shut down Trump rallies, but "at the end of the day in any campaign, responsibility starts at the top. And it is not beneficial when you have a presidential candidate like Donald Trump telling his supporters, 'Punch that guy in the face.'"

Sen. Marco Rubio, the Florida senator who faces a must-win against Trump in Tuesday's Florida primary, said the businessman exploits Americans' anger and anxieties with conspiracy theories and exhortations that can appeal to those who are unbalanced.

"There are people out there that listen to this stuff and we don’t know how they’re going to react," Rubio said on ABC's This Week. "And he keeps putting this stuff out there. We’re going to have an ugly scene here; we already have seen these ugly scenes."

On CBS, Trump said "I don't condone violence," but added that the punching victim in North Carolina "had a certain finger up in the air" and his supporter got angry.

Trump told NBC that he is looking at paying the legal fees of the North Carolina puncher who was later arrested by police: “I've actually instructed my people to look into it, yes.”

Many of his supporters are angry, Trump said, but only at the country's failures that have damaged the economy.

"It is anger against incompetence," Trump said on CNN's State of the Union.