“I would never mock a person that has difficulty, I would never do that, I’m telling you, I would never do that, I would never do that,” Trump told supporters at a rally in Sarasota, Fla., on Saturday.
“I would never do it. I don’t care if I liked the person or didn’t, and I don’t know this person,” he added.
The billionaire business mogul said he was trying to pantomime a reporter “groveling” when he flailed his arms around on stage at a rally in South Carolina last week.
Kovaleski has a chronic condition that impairs the movement of his arms. 
The Times called Trump’s behavior “outrageous.”
Trump demanded an apology from the Times over the allegation.
“I think, frankly, the New York Times should give me an apology,” he said. “I do. I think they should give me – and I’d love to have the apology before they go out of business. I would love it. I would love it.”
Trump accused Kovaleski of using his disability to his advantage.
“The problem is, he’s using what he’s got to such a horrible degree, I think it’s disgraceful,” he said.
The Republican primary front-runner cited an article written by Kovaleski for the Washington Post in 2001 that appeared to corroborate his claim that Muslims in New Jersey were “dancing in the streets” after the 9/11 terrorist attacks on the World Trade Center.
Kovaleski later renounced the report, prompting Trump's "groveling" imitation of the journalist.
A woman who appeared to be a protester briefly interrupted Trump during the opening moments of his remarks. It was not clear what she say saying.
The businessman encouraged security to escort her out of the arena safely.
“Be nice, be nice, be nice, be nice to the person, be nice, be nice to the person, don’t hurt the person,” he said.
“Please nicely escort the person out, please, thank you. Escort the person out please.”
Trump bragged that he was able to handle the situation diplomatically, after a protester who interrupted his rally last week was tackled to the ground.
“Do you see how diplomatic I’ve become, right?” he said. “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,” he added. “So, today, you’re my witnesses, could I have been nicer?”
Trump seemed to deliberately invoke the president’s middle name, claiming that future generations are “going to know about Barack Hussein Obama” when they look back at today’s financial problems.
“They're going to be thinking about, 'Obama really blew it,’ ” he said.
Trump addressed supporters outside of the arena before making his way to the main stage, inviting children to ride up and down in his helicopter.
The pre-rally festivities included an elephant outside of the arena with “Trump: Make America Great Again” painted on its side.
- Updated at 4:06 p.m.