In attempting to refute the claims, the president's lawyer, Barry Zuckerkorn Rudy Giuliani, said that he talked to witnesses to the Trump-Cohen conversation about the Trump Tower meeting, and it was, um, it was not about the Trump Tower meeting (?).
"Sounds to me like someone is trying to make up stories in order to get himself out of an unrelated jam (Taxi cabs maybe?)" Trump tweeted.
The US president has repeatedly denied all knowledge of the encounter, but according to television networks CNN and NBC, his former lawyer Michael Cohen says Donald Jr told his father about the Russian offer and that Trump approved.
Sources say Cohen thought he deserved to be campaign manager when Paul Manafort was ousted.
During his televised appearances Sunday, Giuliani continued to rail against Trump's former personal attorney, telling CBS, "I don't see how you can believe Michael Cohen", and accusing Cohen of violating Trump's attorney-client privilege.
CNN reported that Cohen claims he was present, along with several others, when Trump was informed of the Russians' offer by Trump Jr.in 2016. Giuliani continued, "One is with the President of the United States".
Even Steve Bannon, the former White House chief strategist and top Trump campaign official, said the meeting was "treasonous" and speculated that "the chance that Don Jr. did not walk these (Russians) up to his father's office on the twenty-sixth floor is zero".
Trump has denied ever having a relationship with McDougal, and Giuliani has said the tape shows Trump was hearing about the payment for the first time when Cohen brought it up. As we now know, Trump Jr. later acknowledged that it clearly wasn't just about adoption.
Contacted by CNN, one of Cohen's attorneys, Lanny Davis, declined to comment.
The moves suggested that Mr. Cohen is looking for a way out of looming trouble.
The New York Times has reported that Mueller is investigating whether Trump's tweets about Attorney General Jeff Sessions and former Federal Bureau of Investigation director James Comey constitute an attempt to obstruct justice. While his private recordings of Trump and others have been seized by investigators, he has not yet produced evidence to support his claim that Trump knew of the Trump Tower meeting.
Giuliani also said negotiations have momentarily paused with Mueller over a potential voluntary interview with the president.
Previously Trump has denied knowing in advance that the Trump Tower meeting was going to take place, and he has denied that there was any collusion between his campaign and Russian Federation.
Mr Trump's denial about his knowledge of the meeting comes as Russian President Vladimir Putin said he had invited Mr Trump to Moscow, and that both he and Mr Trump were ready for further summits, but that conditions needed to be right for a meeting to take place.
"I think there's a reason why the press and the media continue to invite us to come on television and talk about this case", Mr Avenatti added.