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Senator Ted Cruz of Texas said on Friday that Donald J. Trump bore responsibility for “creating an environment” that encourages violence at his events.

Speaking to reporters at a local Republican dinner outside Chicago, where Mr. Trump had just canceled a rally amid fierce confrontations between his supporters and protesters, Mr. Cruz began by saying that the “protesters who took violence into their own hands” were responsible for the episode.

“But in any campaign, responsibility starts at the top,” Mr. Cruz continued. “And when you have a campaign that disrespects the voters, when you have a campaign that affirmatively encourages violence, when you have a campaign that is facing allegations of physical violence against members of the press, you create an environment that only encourages this sort of nasty discourse.”

Mr. Cruz invoked the protests and violent police run-ins at the 1968 Democratic National Convention in Chicago, and predicted that future skirmishes were likely.

“When the candidate urges supporters to engage in physical violence, to punch people in the face, the predictable consequence of that is that it escalates,” Mr. Cruz said. “And today is unlikely to be the last such instance.”

Mr. Cruz also suggested that President Obama had stoked tensions since taking office, arguing that the president had “sought to divide us on racial lines, on ethnic lines, on religious lines, on class lines” in moments of crisis.

“America’s better than this,” Mr. Cruz said.

Though Mr. Cruz also attracts many supporters who are angry with Mr. Obama and Washington politics, his rallies have not veered toward violence. But at the debate on Thursday, Mr. Cruz declined an opportunity to condemn Mr. Trump for the tenor of his events. The senator did criticize his rival for asking supporters to raise their hands in a pledge to vote for him.