Former porn star Stormy Daniels' - whose name is Stephanie Clifford - also has stated she signed a nondisclosure agreement regarding her one-time alleged sexual encounter with Donald-trump at 2006.
Later Tuesday, Avenatti said he and Daniels will "fully cooperate with any search for the truth".
Several former officials at the Federal Election Commission have said the payment appears to be a violation of campaign finance laws, and multiple Washington-based groups have filed complaints with the FEC, urging it to investigate.
Hours after the raid was conducted, Trump commented that the incident was a "disgrace" and an "attack on our country".
The person familiar with the investigation, who wasn't authorized to discuss it and spoke on condition of anonymity, said the probe by the public corruption unit of the U.S. Attorney's office in Manhattan is trying to determine if there was any fraud related to the payments.
Federal agents additionally searched documents on ex-Playboy model Karen McDougal, who obtained £150,000 in the parent corporation from The National Enquirer, the Journal claimed. Federal officials have not commented on the raid, and it is not clear whether it was related to Mueller's investigation of alleged collusion between the Trump campaign and Russian Federation.
Since Sessions recused himself from the Russian election probe, Deputy Attorney General Rod Rosenstein would have been the one to ask judges to approve the Federal Bureau of Investigation raid on Cohen's office.More news: Kim Jong-un breaks silence on talks with Donald Trump
More news: Avengers: Infinity War stars assemble to stop spoilers
More news: Caster leads SA at Commonwealth opening ceremony
Getting a warrant approved is not easy, said Donald K. Stern, a former United States attorney in MA who is now managing director of Affiliated Monitors in Boston, which provides ethics and compliance advice to companies.
Some White House allies think that this one, like numerous administration's pockets of turbulence, was brought on by Trump himself - specifically, by comments he made last week aboard Air Force One, when he claimed he had no knowledge of the payment Cohen made to Daniels, according to three people familiar with the discussions. 'Or he should have certainly let us know if he was going to recuse himself, and we would have used a - put a different attorney general in'.
After Buzzfeed past year published the contents of the Russian "dossier", Cohen in January sued the publication and a consulting firm, Fusion GPS, that produced it because the document alleged that he met with a Russian official in Prague, among claims about possible collusion between Russia and the campaign. "Angry and increasingly isolated, the president is more unpredictable than ever", reported Politico this week, in one of many behind-the-scenes accounts portraying Trump as being driven to distraction by this latest development. Many in the president's orbit think Rosenstein's position is now the most endangered if the president decides to take action to try to halt the probe, according to people familiar with the situation. "It is a total witch-hunt, I have been saying it for a long time", he told reporters.
Asked if he wants to fire Mr Mueller, Mr Trump replied: "We'll see what happens".
Cohen admitted in February that he had facilitated a payment to Daniels, although he has denied the validity of the alleged affair.
The Times has said Deputy Attorney General Rod Rosenstein, a Philadelphia native and Trump appointee, authorized the raids.
It wasn't just on Twitter where Trump railed against the raid.