Trump vehemently denied Cohen's claim via Twitter.
"I did NOT know of the meeting with my son, Don jr. Sounds to me like someone is trying to make up stories in order to get himself out of an unrelated jam (Taxi cabs maybe?)" the president tweeted Friday morning.
Cohen's attorney, Lanny Davis, declined to comment to ABC News, other than to say an earlier report on the assertion by Cohen wasn't from him.
In an interview with ABC News Chief Anchor George Stephanopoulos earlier this month, Cohen criticized members of Trump's presidential campaign who attended the 2016 meeting.
"I believe it was a mistake by those from the Trump campaign who did participate," Cohen said. "It was simply an example of poor judgment."
Cohen declined in the interview to answer whether Trump knew about the gathering beforehand. "I can't comment under advice of my counsel due to the ongoing investigation by the U.S. Attorney’s Office in the Southern District of New York," he said.
Former New Jersey Gov. Chris Christie, an ABC News contributor, said there would need to be "serious corroboration" to prove that the allegations of Trump's advance knowledge of the meeting are true.
"First off, we don’t know where this came from, we don’t know if this is anything Michael Cohen really is even willing to say because the response of his legal team was, 'Not us, it didn’t come from us' And then you don’t even know if it’s true," Christie said in an interview Friday with Stephanopoulos on "Good Morning America."
"If it’s true, then everybody’s got some more questions to answer," Christie continued. "But again, remember this too, if it’s just one person, you know, corroborating this kind of stuff is very difficult. And especially if you’re going for the president of the United States, you better have some pretty serious corroboration."
Cohen's claim comes as special counsel Robert Mueller continues to investigate an array of allegations tied to Trump, including whether his campaign officials colluded with Russians in an effort to win the 2016 presidential election. Trump has repeatedly disparaged Mueller's probe as a "witch hunt."
In a series of tweets Friday morning, the president said, "The highly conflicted Robert Mueller and his gang of 13 Angry Democrats obviously cannot find Collusion" and "the only Collusion with Russia was with the Democrats."
Mueller himself has been a registered Republican in the past and was first appointed to his past position as FBI director by GOP President George W. Bush.
Federal Elections Commission records show that some on Mueller's team have donated money to Democratic causes. But Justice Department guidelines prohibit it from considering party affiliation in personnel decisions.
ABC News' Morgan Winsor contributed to this report.