He said the search warrant describes the investigation as an investigation into a possible violation of foreign lobbying rules.
In the weeks before the November election, the contents of Hunter Biden's laptops were leaked to the media. During the call, Trump urged his counterpart to get in touch with Giuliani, who "very much knows what's happening and he is a very capable guy", according the notes released by the White House.
Mr Cohen admitted to lying during congressional testimony about the timing of discussions around an abandoned plan to build a Trump Tower in Russian Federation.
"This is not the type of law enforcement action that is done on a whim", said Christopher Ott, a former federal prosecutor.
Giuliani could not immediately be reached for comment.
Federal prosecutors in Manhattan had pushed a year ago for a search warrant for records, including some of Giuliani's communications, but officials in the Trump-era Justice Department would not sign off on the request, according to multiple people familiar with the investigation who insisted on anonymity to speak about an ongoing investigation.
Giuliani first became well-known in the 1980s as US attorney in Manhattan, the same office that is now investigating him.
Investigators executed warrants on Wednesday morning (Late Wednesday or early Thursday AEST) at Mr Giuliani's home on Madison Avenue and his office on Park Avenue and seized electronic devices, a person familiar with the investigation told the AP.
Giuliani's role in Washington was complex, with the former mayor frequently proclaiming himself a business consultant and lawyer in the private sector even as he enjoyed extraordinary access to the halls of power.
The New York Times and other media outlets pointed out that although the search warrant doesn't indicate that Giuliani committed a crime, it shows that investigators convinced a judge that a criminal act may have occurred, and that a warrant could help retrieve further evidence. The Justice Department requires that applications for search warrants served on lawyers be approved by senior department officials.
Giuliani's involvement took place before, during and then after the core events of the Ukraine affair in 2019 in which Trump ordered assistance be frozen to extract concessions from Ukraine's government.
Because the former mayor is a practicing attorney, the Justice Department's leaders would also have to weigh in and establish a special team of agents and prosecutors to review evidence for attorney-client information, former prosecutors said. Biden's son, Hunter, was facing intense scrutiny for his suspicious position on the board of a nefarious Ukrainian gas company, Burisma, despite having no relevant experience in the industry. Cohen ultimately pleaded guilty to eight federal charges, including campaign finance fraud, and was sentenced to three years in prison.