Republican Rivals Call on Trump to Take Responsibility for Violence "I should point out there isn’t violence at my events," Marco Rubio said.

"I think a campaign bears responsibility for creating an environment, when the candidate urges supporters to engage in physical violence to punch people in the face," Sen. Ted Cruz said, speaking to reporters at Rolling Meadows, Illinois. "The predictable consequence of that is that it escalates. And today is unlikely to be the last such instance...That's not how our politics should occur.

"You know, the city of Chicago in 1968, saw some ugly days when politics descended into hatred and instability and even violence. It is my hope that in 2016 we can appeal to our better angels and avoid going down that road once again."

Protesters and Trump supporters clashed outside an event in St. Louis and there were several scuffles inside the UIC Pavilion in Chicago. Trump has drawn fire for remarks that apparently encouraged violence against protesters, including saying in one instance that he wanted to punch someone in the face.

Five people were arrested, and two police officers were injured, Chicago Police said.

Sen. Marco Rubio argued it's Trump's rhetoric that is inciting violence at his events.

"I should point out there isn’t violence at my events," Rubio said. "There isn’t violence at Ted’s events. There isn’t violence at a Kasich event. There isn’t violence at a Clinton event."

"There is only one presidential candidate who has violence at their events. And I do think Donald needs to realize and take responsibility for the fact that some of the rhetoric he has used could be contributing to this environment that is growing increasingly disturbing for a number of Americans," Rubio told ABC News at a media availability in Naples, Florida.

Before news broke of Trump's rally being postponed, Ohio Gov. John Kasich told reporters while campaign in Moraine, Ohio was asked if he was concerned about the violence at Trump rallies.

"We don't want to have violence at any rally,” Kasich answered. "We don't have them at our rallies, but I just can't comment on what the heck has happened at his rallies. I've never been to one, don't expect to be going.”

Trump told CNN Friday night after postponing his rally that he doesn't "condone violence and it is not acceptable to me." He made similar remarks a the most recent presidential debate.

Trump also said on CNN that "we've been very mild with protesters."

"Nobody has been hurt at our rallies," he added.

Additional reporting by Ben Gittleson and Brad Mielke.