Stormy Daniels's lawyer Michael Avenatti claimed Tuesday that President Trump is "scared" of the adult-film star, who recently went public about an affair she claims to have had with the president more than a decade ago.

"We didn't think that he would stay silent this long and I think it's pretty clear he is scared of my client and perhaps of me," Avenatti said of Trump on MSNBC. "And he should be."

Avenatti speculated that Trump might be staying quiet because Daniels, whose real name is Stephanie Clifford, might not be "punching hard enough" or - more likely, he argued - because the president knows the allegations are true.

"It is the same reason why he didn't sign the agreement, so he can later claim that he didn't know anything about it," Avenatti said, referring to a nondisclosure deal that Daniels reached with a personal lawyer for Trump shortly before the 2016 election.

Daniels appeared on "60 Minutes" on Sunday where she talked about the details of her alleged affair with Trump in 2006, saying she was threatened years ago to not go public with the allegations.

According to Avenatti, there is a more information that did not make it into Daniels's "60 Minutes" interview.

"There is a lot of embarrassing information that has yet to come out," Avenatti said.

"There is a mountain-load of evidence, and so perhaps that is why he is continuing to deny it," he added, referring to the president.

Daniels accepted $130,000 as part of a nondisclosure agreement she signed with Trump's lawyer, Michael Cohen, a month before the 2016 election that prevented her from discussing the alleged affair.

However, Daniels has argued that the contract is void because Trump did not sign it, freeing her to discuss the alleged affair.

Trump's lawyers maintain that Daniels is liable for $20 million in damages for breaking the agreement, while Daniels's lawyer has hinted in recent days that hard evidence of the affair exists.