SARASOTA, Fla. -- Republican front-runner Donald Trump on Saturday repeated his call for the New York Times to apologize over accusations that he mocked a disabled reporter at a rally earlier this week.

"I think the New York Times, frankly, should give me an apology," he told a cheering crowd of several thousand at an arena in Sarasota, Fla.

"Who else is going to take on the New York Times? I don't care. I don't care," he said, mocking the company's business decisions and financial standing. "They'll probably be out of business pretty soon."

Trump again accused Times reporter Serge Kovaleski of backing down from a story he wrote for The Washington Post in 2001, in which he reported that local authorities had investigated claims that Muslims in New Jersey had been seen cheering the Sept. 11 terrorist attacks. Trump cited the report, which did not say authorities had found evidence substantiating the accounts, to back up his claim that he had personally witnessed thousands of Muslims celebrating the attacks.

The billionaire has been criticized for appearing to mock Kovaleski, who suffers from a congenital joint condition, at an event in South Carolina earlier this week. On Thursday, Trump accused the reporter of using his disability to "grandstand."

"This reporter is so happy. Because people have heard of him now," Trump said Saturday. "Nobody ever heard of the guy."

Kovaleski has said he stands by his original story. Trump's claim that the celebrations occurred has been denied by law enforcement and government officials who were in the state in the days and weeks that followed the attack on the World Trade Center.

"I took a lot of heat about a reporter. And what really happened? I think it's important for me to say," said Trump, who said he was mimicking what he called Kovaleski's "groveling," not his physical condition.

"I was talking about groveling. A reporter is groveling because he took back the statement that he wrote 14 years ago," he said.

"I don't mock people. I don't mock people. I don't mock people that have problems. I don't mock people that have problems, believe me," he said. "Now, people mock me with my hair..."

Trump also doubled down on his initial claim. "I talked about Muslims celebrating in New Jersey. And everyone knows it's true … people saw. So I made that statement. I didn't think it was a big deal because I thought everybody knew, adding that "everybody admits worldwide, Muslims were absolutely going wild" over the events of Sept. 11. He later criticized "Barack Hussein Obama" for the administration's response to terrorist attacks.

On Saturday, Trump also stressed his opposition to gun control, one day after a gunman went on a shooting rampage at a Planned Parenthood clinic in Colorado that resulted in three deaths.

"I just want to say it up front, right now, Second Amendment 100 percent," Trump told the cheering crowd at a Sarasota campaign rally. "Remember it. … Second Amendment up, up up."

Trump didn't directly mention Friday's shooting in Colorado Springs, pointing instead to the terrorist attacks in Paris earlier this month.

"If some of those folks that were just slaughtered in Paris, if a couple of guns were in that room that were held by the good guys, you woulda had a different story, let me tell you. You would have had a totally different story -- would have been a different world. And I can say that about a lot of these crazy attacks."

While Trump stood by his criticism of the Times, his unsupported claims about Muslims and his recent support for the Second Amendment, he did shift his tone on at least one front: his response to protesters, several of whom interrupted his remarks Saturday, a week after a Black Lives Matter protester was beaten at a Trump rally in Birmingham, Ala.

"Please nicely escort the person out, thank you," Trump instructed security from the podium Saturday. "Alright please, nicely escort the person out, nicely, Very nicely. … come on, you can go faster than that," he said, as the crowd booed.

"Do you see how diplomatic I've become? Right?" he told the crowd after the protesters had left. "Because at the last rally we had one person — we had 15,000 people, we had one person who was really, really being bad. Really being bad. And it was horrible. It was horrible. And we said get him out, get him out. We were a little bit rough, and I got criticized, so today, you're my witness. Could I have been nicer than that?"

On Monday, Trump plans to appear in New York with a group of African American evangelicals before heading to a campaign rally in Macon, Ga.