In his statement, Avenatti says he and Daniels "will fully cooperate with any search for the truth regarding the threats, cover-up and lies concerning the NDA and $130k payment".
Federal Bureau of Investigation special agents, working under the authority of the USA attorney in Manhattan, seized records relating to Karen McDougal, the former Playmate who said she had a 10-month affair with Trump, and Stephanie Clifford, the porn star known as Stormy Daniels, who said she had sex with Trump just once, according to the person.
The New York Times, which first reported the news about the two women, said the search warrant for the Federal Bureau of Investigation raids also sought information about McDougal, who was paid $US150,000 by the parent company of The National Enquirer tabloid, which then withheld a story about her relationship with Trump.
Those who say the media shouldn't cover the tabloid saga of Stormy-who just sold an interview and nude photo shoot to Penthouse-say most Americans don't care if she and Trump had one sexual encounter in 2006.
McDougal was paid $150,000 in the summer of 2016 by the parent company of the National Enquirer under an agreement that gave it the exclusive rights to her story, which it never published.Cohen said he paid Daniels $130,000 in exchange for her silence about her claim to have had a one-night-stand with Trump.
Trump's advisers have spent the last 24 hours trying to convince the president not to make an impulsive decision that could put the president in more legal jeopardy and ignite a controversy that could consume his presidency, several people close to Trump said.
White House press secretary Sarah Huckabee Sanders equated the effect of the investigation and Russia's support for Syrian dictator Bashar Assad. He bitterly complained that the raids were meant to ruin Cohen's life and expressed frustration that it was another front from which to attack his presidency, according to a person familiar with the conversations but not permitted to discuss them publicly. The raid on Cohen was not carried out by special counsel Robert Mueller's team.
Trump also revived his broadsides on Rosenstein as well as Rosenstein's boss, Attorney General Jeff Sessions, whom he belittled to confidants for recusing himself from the investigation and, in turn, delivering him to Mueller. But the raid was prompted, at least in part, by evidence or allegations uncovered by Mueller's team.
McKay said Trump's ability to invoke the privilege is "no different" from anyone else's.
Senate Judiciary Committee Chairman Chuck Grassley says it would be political "suicide" for President Donald Trump to fire special counsel Robert Mueller. Rosenstein has repeatedly said he has not seen any reason to dismiss Mueller.
Cohen has said he paid Daniels out of his own pocket shortly before the 2016 presidential election, but has not explained why.
White House attorney Ty Cobb and White House Counsel Donald McGahn have repeatedly sought to dissuade Trump from firing Mueller and renewed their efforts after the raids, two USA officials familiar with the discussions told Reuters.
Agents also seized records related to a $130,000 payment made to Daniels, who says she had sex with Trump the same year as McDougal.
The U.S. Attorney's office in Manhattan made the filing after lawyers for Cohen and Trump asked a judge on Friday to block investigators from reviewing material the Federal Bureau of Investigation seized in a search of Cohen's office and residence on Monday.
The raids infuriated Trump, who tweeted "Attorney-client privilege is dead!" on Tuesday.