Baldwin has strenuously denied a New York Post reporter's accusation that the 30 Rock actor threatened her and used a racial epithet about her African-American photographer during an altercation on Sunday.
"He wants to say I used some racial slur against him... The Post will stop at nothing - that's what The Post is. Their function is to denigrate people, humiliate people, reduce people, make excuses for people who are their political partisans," Baldwin later told Gothamist.
His 30 Rock co-star Morgan was asked about the controversy on the Drex and Maney Show, where he said Baldwin was acting inappropriately if in fact he did utter the slur.
"If [Alec] called somebody a c**n, he should apologise," Morgan noted.
Morgan also stressed that there is no place for racial slurs to be used in modern society.
"First of all, c**n is played out," Morgan insisted. "That goes for anybody. If another black person calls somebody a c**n, he should apologise ... IF he did it."
Morgan himself issued a public apology in 2011 for making a string of homophobic comments during a comedy show in Nashville.
There have been reports that an audio recording of the incident does not include any racial slur being uttered by Baldwin, although that information is still unconfirmed.
New York State Senator Malcolm Smith has called for Baldwin to be banned from television and movies if it is found that he did use the slur.
Baldwin has suggested that he will be taking a break from Twitter in the wake of the scandal.