The interest in Cohen's records related to the Access Hollywood incident was first reported by the New York Times.
Prosecutors are investigating whether Cohen engaged in bank fraud, wire fraud and violations of campaign finance law, as the Washington Post previously reported.
Stephen Ryan, a lawyer for Cohen, has called the raids "inappropriate and unnecessary," saying Cohen has cooperated completely with all government entities investigating Russia's interference in the 2016 election.
The probe into Cohen, which was referred by Special Counsel Robert Mueller to the US Attorney's office for the Southern District of New York, appears to be focused in part on the lawyer's involvement with payments made to two women who alleged affairs with Trump.
The search warrant executed on Tuesday sought all of Cohen's communications about payments or negotiations with adult-film star Stormy Daniels and ex-Playboy model Karen McDougal.
In the Access Hollywood video, Trump is heard on a live microphone bragging in extremely vulgar terms about groping and kissing women without their consent.
"When you're a star, they let you do it," Trump says in the video, speaking to Access Hollywood host Billy Bush. "You can do anything."
The recording was an outtake from a segment that the celebrity-TV show shot in 2005 when Trump had a cameo on Days of Our Lives. Trump, who at the time was starring on NBC's The Apprentice, was making a guest appearance - playing himself - on the NBC soap opera.
The Post revealed the existence of the recording on October 7, 2016. On that day, Trump first sought to downplay the comments as "locker-room banter," but later that night he apologised for his remarks.
On the same day, the US intelligence community released a statement formally blaming Russia for interfering in the 2016 election.
Less than an hour after the Post's story, WikiLeaks posted the first set of emails stolen from Democratic nominee Hillary Clinton's campaign chairman John Podesta.
US intelligence officials later blamed the Russian Government for the hack of Podesta's email.
