"The sad part about it is, it didn't in the slightest bit jar or surprise me that Donald Trump would do something this low-rent, given his track record," Kovaleski said.
People who were upset by Trump's actions have taken to Twitter to express their concerns.
Trump campaign spokeswoman Hope Hicks declined to comment on the record about the incident. A campaign official speaking on background said Trump was "not aware of any condition and was not mocking his physical appearance in any way."
In a phone interview Wednesday, Kovaleski said he's sure Trump remembers him - and his condition.
In his speech Tuesday, Trump defended his recollection of the Muslim revellers by citing a 2001 article by Kovaleski, who worked for the Washington Post at the time, noting that "authorities detained and questioned a number of people who were allegedly seen celebrating the attacks and holding tailgate-style parties on rooftops while they watched the devastation on the other side of the river."
Those allegations were never corroborated but have persisted in online rumors in the 14 years since the attacks. In an interview on CNN this week, Kovaleski said he did not recall "anyone saying there were thousands, or even hundreds, of people celebrating."
That was the comment Trump was mocking in his speech. According to the campaign official, Trump "was merely emphasising the uncertainty of the verbal/written statement provided by the reporter in regards to his article."
This is not the first time Trump has been panned for apparently mocking a person's physical disability. In a July interview with NBC news, Trump lashed out at columnists Jonah Goldberg and Charles Krauthammer. Krauthammer had called the candidate a "rodeo clown."
"I get called by a guy that can't buy a pair of pants, I get called names?" Trump said at the time.
Krauthammer is paralysed from the waist down.
Kovaleski's friends and colleagues took to social media this week to defend him - and excoriate Trump.
"@sergenyt is one of the best reporters-- and best people-- I know. This is despicable," ESPN reporter and author Don Van Natta Jr. wrote on Twitter.
"The measure of men. Know this: Serge Kovaleski, aka @sergenyt, is a journalistic rock star and one great colleague," wrote Times reporter Dan Barry.
The Times also issued a sharply worded statement Wednesday: "We think it's outrageous that he would ridicule the appearance of one of our reporters," a spokesman for the Times said.
Late Wednesday, Trump tweeted this rejoinder: "The failing @nytimes should be focused on good reporting and the papers financial survival and not with constant hits on Donald Trump!"
