Essential Consultants was created by Cohen days earlier. He used it in the coming weeks and months to collect millions of dollars in consulting fees from corporate clients like AT&T, Swiss drugmaker Norvatis and Columbus Nova, which described itself as an affiliate of a conglomerate known to be owned by a Russian oligarch.

"Once again Mr. Giuliani has attempted to deceive the American people with this payment," said Michael Avenatti, Daniels' new lawyer, who is trying to break the nondisclosure agreement in court.

In a follow-up interview, Giuliani said that he did not know how Cohen had paid Daniels ? "Lawyers do things under LLCs all the time," he said ? and that he had correctly anticipated that the OGE would rule that Trump had needed to disclose the $130,000 as a loan. That is why, he said, he decided to disclose it himself.

The FBI and federal prosecutors from the Southern District of New York are investigating Cohen. They removed documents and electronic equipment from Cohen's offices using a search warrant last month, although he has not been charged with any crime.

Special Counsel Robert Mueller, meanwhile, continues his year-old investigation into possible collusion between Trump's campaign and Russian intelligence services, which were actively working to help Trump win in 2016.

Rosenstein appointed Mueller after Trump first fired FBI Director James Comey, and then shortly thereafter told both NBC News and Russian diplomats visiting the Oval Office that he had done so because of the FBI's Russia probe.

Trump has repeatedly called the Mueller probe a "witch hunt" spurred by Democrats angry that they had lost an election they believed they would win. Giuliani, who was once the U.S. attorney leading the office now investigating Cohen, makes that same argument and says news outlets that cover the Mueller investigation and the Stormy Daniels payment are treating Trump unfairly.