Chicago (CNN) Donald Trump's campaign on Friday postponed a rally in Chicago amid fights between supporters and demonstrators, protests in the streets and concerns that the environment at the event was no longer safe.

The announcement, which came amid large protests both inside and outside the event at the University of Illinois at Chicago, follows heightened concerns about violence in general at the GOP front-runner's rallies. Illinois holds its Republican primary on Tuesday.

Hundreds of demonstrators packed into an arena, breaking out into protest even before Trump had shown up. At least five sections in the arena were filled with protesters.

"Mr. Trump just arrived in Chicago, and after meeting with law enforcement, has determined that for the safety of all of the tens of thousands of people that have gathered in and around the arena, tonight's rally will be postponed to another date," the Trump campaign said in a statement. "Thank you very much for your attendance and please go in peace."

Several fistfights between Trump supporters and protesters could be seen after the announcement, as a large contingent of Chicago police officers moved in to restore order.

Supporters of Trump still inside chanted "We want Trump" after the event was canceled. Protesters, meanwhile, shouted "We shut s*** down" and "We stumped Trump." Others chanted "Bernie" as supporters whipped out Bernie Sanders campaign signs.

The scene here after @realDonaldTrump canceled his Chicago rally. Protesters celebrate chanting "We stopped Trump" pic.twitter.com/EDRxcKtwGr — Jeremy Diamond (@JDiamond1) March 12, 2016

Some protesters were being detained and forcefully carried out.

Maria Hernandez, a 25-year-old community organizer, broke out into dance as a Trump campaign staffer announced that the rally had been canceled.

"I've never been more proud of my city," Hernandez told CNN.

Hernandez, who came out to protest Trump, said the Republican front-runner's immigration policies, as well as racial divisions in her city, pushed her to show up and protest Trump's planned event.

"I'm protesting because I'm black and Mexican and I'm not sure where he wants to deport me to, but I deal with racism daily in Chicago and I've had enough," she said.

One Trump supporter said he was "disappointed" that the event was postponed.

"Protesters have won now," Marlin Patrick, 55, told CNN. "We just feel as if the protesters have taken over."

Debi Patrick, a 53-year-old Trump supporter who lives outside Chicago, said there should have been more security planned for the event, but said she didn't blame Trump for the atmosphere at the rallies, saying people are responsible for their own behavior. Asked if she would still vote for Trump on Tuesday, she said, "Absolutely, more than ever."

But, Patrick said, "This is scaring the hell out of me, trying to leave here."

JUST WATCHED Donald Trump speaks out after clashes Replay More Videos ... MUST WATCH Donald Trump speaks out after clashes 02:35

"Until today, we've never had much of a problem," Trump later told CNN's Don Lemon. Asked if he had any regrets about the charged rhetoric at his rallies, Trump was defiant.

"I don't have regrets," Trump said. "These were very, very bad protesters. These were bad dudes. They were rough, tough guys."

Authorities made five arrests, said Chicago Interim Police Superintendent John Escalante.

One of those arrested was Sopan Deb, a CBS reporter covering the Trump campaign. He's the latest reporter to be involved in incidents at Trump events, including Time magazine photographer Chris Morris (who claimed a Secret Service agent choked him and slammed him the ground) and Breitbart reporter Michelle Fields (who filed charges against Trump's campaign manager for allegedly grabbing her).

Regarding Thursday, CBS News President David Rhodes defended his reporter who was charged with resisting arrest, tweeting, "On tape, you see he did not resist, identified himself as working press."

.@SopanDeb was handcuffed, later charged with resisting arrest; on tape you see he did not resist, identified himself as working press — David Rhodes (@davidgrayrhodes) March 12, 2016

Two officers suffered injuries, he said. One was hit in the head with a bottle.

Some 300 officers were on hand for crowd control, according to Escalante. The Trump campaign didn't consult with authorities before calling the event off, he said.

The Chicago Police Department was "confident" they could provide adequate security to protect Trump, his supporters and protesters, Escalante said.

Mayor Rahm Emanuel praised officers' effort under difficult circumstances.

"For all of us who cherish the ideals upon which our country was founded, the hateful, divisive rhetoric that pits Americans against each other demeans our democratic values and diminishes our democratic process," he said in a statement.

"I want to thank the men and women of the Chicago Police Department for their hard work tonight in unexpected circumstances, and their continued commitment to protecting people's first amendment rights."

A crowd of protesters outside the rally site had been steadily growing throughout the afternoon. Earlier Friday, 32 people were arrested in protests both inside and outside Trump's rally at the Peabody Opera House in St. Louis, police said. Thirty-one people were charged with disturbing the peace, and one was charged with third-degree assault. St. Louis police declined to provide further details.

Protests spill into streets

Soon after the event was postponed, scores of protesters -- a racial mixture of whites and blacks, Hispanics and Asians -- spilled out into the streets near the university, which is located in the city's downtown.

Dozens of protesters gathered outside a parking garage adjacent to the arena, where police set up a human barricade to allow supporters to go to their cars and leave. More than a dozen police officers on horseback were there.

"Let's go, let's go," one Chicago police officer told Trump supporters in a truck. "Go home."

One supporter, who didn't give his name as he drove out, said the situation was dangerous and that he felt unsafe as protesters shouted at his car.

At one point, a man on the third floor of the garage leaned over the edge and shouted at protesters, "I don't support Trump."

A protester responded, "You f***ing neo-Nazi prick, come down here."

Aureliano Rivas, 18, a Mexican-American high school student from Chicago, told CNN he was protesting because "we have to stand our ground."

1 of protesters out here: "If I'm able to spread my message, I'm going to stay out here as long as everybody else" pic.twitter.com/wWQIYHm5Ns — Jeremy Diamond (@JDiamond1) March 12, 2016

"We shouldn't let racism happen like this," said Rivas, who was shouting "F*** Trump" as Trump supporters drove out of the garage. In response, Rivas said, supporters were flipping him off.

Asked what he would tell a Trump supporter, Rivas said, "This is wrong. You shouldn't support someone who is racist."

Trump responds

Earlier in the night, as protests outside the arena continued, Trump tweeted that he had "just got off the phone with the great people of Guam," which holds a Republican convention on Saturday to elect delegates

"I just got off the phone with the great people of Guam! Thank you for your support! #VoteTrump today! #Trump2016."

After the protests in the arena ended, Trump did a series of media interviews, including one with CNN's Lemon. Trump said he had no regrets about his rhetoric, attributing the root cause of the violence to economic issues such as unemployment among African-American youths.

"We have a very divided country," Trump said. "A lot of people are upset because they haven't had a salary increase for 12 years."

Trump also blamed the media for what he saw as an overinflation of the evening's problems. And he said most incidents involving protesters are tame and in control, saying that he has been "very mild" with those who disrupt his events and that his events are gatherings of "great love" that are interrupted by unruly, violent people.

Trump, however, did say he hoped "my tone is not that of causing violence."

"My basic tone is that of securing our borders, of having a country," he said.

And on Saturday morning, Trump took to Twitter again to blast those who disrupted the event. Their efforts would backfire and spur others to rally even more to support him, he predicted.

The organized group of people, many of them thugs, who shut down our First Amendment rights in Chicago, have totally energized America! — Donald J. Trump (@realDonaldTrump) March 12, 2016

He wrote, "The organized group of people, many of them thugs, who shut down our First Amendment rights in Chicago, have totally energized America!"

2016 hopefuls blast Trump

The Republican frontrunner's son, Donald Trump Jr., blamed the demonstrators for the unrest.

"Liberals love the first amendment until you say something they don't agree with," he tweeted.

Liberals love the first amendment until you say something they don't agree with. — Donald Trump Jr. (@DonaldJTrumpJr) March 12, 2016

Yet Texas Sen. Ted Cruz, Trump's main rival for the GOP presidential nomination who declined at CNN's Republican debate this week to blame Trump for violence at his rallies, took a much sharper tone on Friday night.

"In any campaign, responsibility starts at the top," Cruz told reporters in Rolling Meadows, Illinois.

"When you have a campaign that affirmatively encourages violence," he continued, "you create an environment that only encourages that sort of nasty discourse."

Cruz added that the violence was a "predictable consequence" of Trump's posture toward protesters at his events.

Florida Sen. Marco Rubio told Lemon that the protests were part of an "organized effort to disrupt a rally. This is not some organic protest."

"But putting that aside for a moment, the tone and tenor of Donald Trump's rallies over the last few months has been disturbing to a lot of people," he continued.

Rubio added, "If you're running for president, you have to understand that that kind of rhetoric from a president -- or a major presidential candidate -- has ramifications," Rubio said. "The images that the world must be looking at now must seem to them like our republic is fracturing."

Ohio Gov. John Kasich blasted Trump in a statement.

"Tonight, the seeds of division that Donald Trump has been sowing this whole campaign finally bore fruit, and it was ugly," he said. "Some let their opposition to his views slip beyond protest into violence, but we can never let that happen."

And Vermont Sen. Bernie Sanders, a Democratic hopeful, tweeted during the night that his campaign's message was about unity, a thinly veiled shot at Trump.

"We do things a little different in this campaign: We bring people TOGETHER. #BernieInIL," he tweeted.

We do things a little different in this campaign: We bring people TOGETHER. #BernieInIL — Bernie Sanders (@BernieSanders) March 12, 2016

Democratic front-runner Hillary Clinton also weighed in, condemning the violence.

"The divisive rhetoric we are seeing should be of grave concern to us all," she said.

"We all have our differences, and we know many people across the country feel angry. We need to address that anger together," according to Clinton. "All of us, no matter what party we belong to or what views we hold, should not only say loudly and clearly that violence has no place in our politics, we should use our words and deeds to bring Americans together."

Heightened tensions at rallies

Protests and racial tensions have recently escalated at Trump rallies. On Thursday, a man attending a Trump rally this week was charged with assault after he allegedly sucker-punched a black protester being led out of a Trump event.

Last fall, Trump said a Black Lives Matter protester maybe "should have been roughed up." And despite an announcement at the start of his rallies urging supporters not to be violent toward protesters, Trump in February urged his supporters to "knock the crap out of" anybody "getting ready to throw a tomato" and vowed to pay for their legal fees should they face charges.

"Knock the crap out of them, would you? Seriously. OK? Just knock the hell -- I promise you, I will pay for the legal fees. I promise, I promise," Trump said

And Trump also said he personally wanted to punch a protester "in the face" during a rally in February.

But at CNN's Republican debate on Thursday, Trump insisted that he did not support violence at his events.

"I certainly do not condone that at all," Trump said, adding, "We have some protesters who are bad dudes. They have done bad things."