Washington (CNN) President Barack Obama lamented a "vulgar and divisive" presidential campaign Tuesday, saying that GOP presidential candidates were setting bad examples for children and tarnishing the United States' reputation abroad.

"In America, there is no law that says we have to be nice to each other, or courteous, or treat each other with respect. But there are norms. There are customs. There are values that our parents taught us and that we try to teach to our children to try to treat others the way we want to be treated," Obama said during a St. Patrick's Day luncheon on Capitol Hill.

Making a barely veiled reference to the rallies of GOP front-runner Donald Trump, Obama described campaign rally scenarios that pit protesters against supporters that has led to "actual violence."

"The longer that we allow the political rhetoric of late to continue, and the longer that we tacitly accept it, we create a permission structure that allows the animosity in one corner of our politics to infect our broader society, and animosity breeds animosity," Obama said.

Trump denies violence

Trump said Monday "there's no violence, nobody's been hurt" at his rallies, which have had a number of high-profile incidents of violence in the past week.

"First of all let's not even use the word violence, there's very little disruption generally speaking. It's a function of the press, the press likes to say what the press likes to say," Trump told CNN's Wolf Blitzer Monday.

"If one person gets up and starts shouting and the police walks that person out, they try and make it like it's a violent thing. It's not violent. It's a protester that stands up or probably a disruptor, because I think they're sent there by people on the other side," he said.

Trump added: "But there's no violence, nobody's been hurt."

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However, Trump repeated Monday that he does not condone violence at his events.

"No, I don't like that. And we don't condone that, Wolf. And I've said that numerous times," Trump said, when asked about the North Carolina supporter who punched the protester.

Obama: GOP should step up

The President was speaking to a bipartisan group of lawmakers, including House Speaker Paul Ryan, who Obama praised for decrying the increasingly bitter campaign trail rhetoric. But the President said more Republicans need to speak out against the language employed by candidates like Trump.

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"We've heard silence from too many of our leaders," Obama said. "Too often, we've accepted this as the new normal. It's worth asking ourselves what each of us may have done to contribute to this kind of vicious atmosphere in our politics."

He said continued use of language that singles out minorities or immigrants could damage America's standing.

"This is also about the American brand. Who are we? How are we perceived around the world?" he said. "The world pays attention to what we say and what we do."

"We can condone this race to the bottom or accept it as the way things are and sink further, or we can roundly reject this kind of behavior if we see it in the other party, or more importantly when we see it in our own party, and set a better example for our children to follow," he said.

RNC officials react

Sean Spicier, communications director for the Republican National Committee, said he agrees with RNC Chairman Reince Priebus that the candidates should all be "talking in a more positive tone."

"We would all like our candidates talking in a more positive tone, more welcoming tone to bring people into our party," he told CNN's Blitzer on Tuesday.

But he added that Obama should be more worried about his own party's politics.

"There's a lot of concern with whether Hillary Clinton's going to be indicted, some of the problems they have here, the momentum that Bernie Sanders has in terms of overtaking her," Spicier said. "I think if the President's concerned, he should keep it to his own party."

Obama praises Ryan

Addressing Ryan, Obama said they had plenty of policy differences, but "I don't have a bad word to say about you as a man."

"We can have political debates without turning on one another, we can disagree without assuming it's motivated by malice," he said. "There are those here who have fought long and hard to create peace in Northern Ireland, and understand what happens when we start going into these dark places, and the damage that can be done and how long it can take to unwind."

"I reject any effort to spread fear or encourage violence or to shut people down when they're trying to speak, or turn Americans against one another," he concluded. "And I think as a citizen who will still be leading this office I will not support somebody who practices that kind of politics."