Avenatti was commenting on a prior appearance on the show by Giuliani, the former New York City mayor who recently joined the president's legal team.
"It is a train wreck. I can't believe that actually just happened,” Avenatti said. "I mean, what we witnessed by Rudy Giuliani may be one of the worst TV appearances by any attorney on behalf of a client in modern times."
On Sunday, in an exclusive interview on "This Week," Stephanopoulos asked Giuliani if Trump learned about the payment to Daniels after Election Day in 2016.
Giuliani said he was not sure when Trump found out, “It could have been recently, it could have been a while back. Those are the facts that we’re still working on.”
Avenatti asserted, however, that “there is no question that this [payment] had everything to do with the campaign.”
“We have evidence that the president knew in the -- in the months at least following the campaign of this payment, certainly knew it long before his statement on Air Force One in April of this year where he effectively stood there and lied to the American people about not knowing anything about this payment,” Avenatti said.
“I mean, any attorney that’s worth anything could have a 30-minute meeting or conversation with his client and get to the bottom of this,” Avenatti added. “This is not a complicated matter that takes months or years to get to the bottom of, George. I mean, this is absurd.”
Avenatti asks if there is a ‘slush fund’
Giuliani also told Stephanopoulos that he doesn't have knowledge of any payments to other women by former Trump lawyer Michael Cohen but that he couldn't rule it out. And he suggested that such payments aren’t uncommon among famous people.
“This is the kind of thing that I’ve settled for celebrities and famous people. Every lawyer that does that kind of work has,” he said.
Avenatti in his interview later in the show asserted that Giuliani seemed to be suggesting that the president's lawyer had "a slush fund" to pay women over extramarital affairs.
"According to Rudy Giuliani, this [type of payment] was basically commonplace," Avenatti said. "The president had effectively an extramarital-affair slush fund that was administered by Michael Cohen, and that [Cohen] would just be expected to take care of these things. They were a regular occurrence."
Daniels' lawyer continued, "I mean, that in and of itself should be very disturbing. Most people of means, most people of wealth and celebrity, they don’t have extramarital affair slush funds and the suggestion is insulting.
Avenatti also disputed the notion that Daniels had sought to cash in on her story by pushing for a payment from Trump before the election.
“That’s absolutely false, that is not what happened. My client was preparing to tell her story. My client did not approach Michael Cohen, did not have anyone approach Michael Cohen,” Avenatti said. “Michael Cohen approached my client and her counsel in an effort to shut her up in the days before the election.”
Asked by Stephanopoulos if he had proof of this, Avenatti responded, “Yes, absolutely, 100 percent.”
“[W]hen the facts and the evidence come out, this is going to be a disaster for Michael Cohen, the president and now Rudy Giuliani,” Avenatti added. “It is time for Rudy Giuliani to be put out to pasture.”