Michael Cohen is President Trump's personal attorney.
But he indicated in a late afternoon tweet Tuesday that he and his client would "fully cooperate with any search for the truth".
Mr Cohen's own lawyer, Mr Stephen Ryan, said agents were working in part on the request of Mr Mueller, the independent prosecutor investigating links between Russian Federation and the Trump campaign.
An anonymous source tells the Washington Post that Cohen is being investigated for possible bank fraud, wire fraud and campaign finance violations.
A furious Trump, who in the last month has escalated his attacks on Robert Mueller's Russian Federation investigation, said from the White House that it was a "disgrace" that the FBI "broke into" his lawyer's office.
"It's a real disgrace", Mr. Trump told reporters, calling the raid and surrounding circumstances, "an attack on our country".
Right-wing commentator Kurt Schlichter said "federal agents are stealing and reading communications between an attorney and his client" and radio host Buck Sexton said, "Attorney client privilege is apparently meaningless in this era of get Trump at all costs".
In this image from video, Michael Avenatti, attorney and spokesperson for adult film star Stormy Daniels, listens to a reporters' question during an interview at The Associated Press, March 21, 2018, in NY. The newspaper identified the second woman as Karen McDougal, an ex-Playboy model who said she had an affair with Trump shortly after the birth of his son in 2006.
Under special counsel regulations, Mueller's office would have to discuss with the attorney general whether to keep an investigation under the special counsel's office or to refer it to a different jurisdiction.
To those that scoffed when we filed this case and claimed it was all about $: As we predicted and as the Federal Bureau of Investigation raid shows, Mr. Cohen and Mr. Trump are in a lot of trouble.
'The attorney general made a bad mistake when he did this, and when he recused himself, ' Trump said. The payment was made by Cohen himself, not Trump, and Trump has denied any involvement - with both Daniels and with the payment. As Cornell Law School's Legal Information Institute explains, the legal concept is meant to keep communications between an attorney and his or her client private.
After Buzzfeed a year ago 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.
"If you know the person who's in charge of the investigation, you know all about that", Trump said.
"I believe it will soon be shown everything I did was legal", added Cohen. The agreement, included as an exhibit to the lawsuit, was reached 11 days before the 2016 presidential election as Trump's campaign grappled with multiple allegations of his sexual misconduct. One Mueller witness, former Trump aide Sam Nunberg, recently connected the special counsel with the payment, saying in an interview on MSNBC last month that prosecutors had asked him about it. That was a witch hunt.
However, in a Off Camera meeting with CNN Tuesday, " Cohen explained: "I am unhappy to own my own personal house and office raided. Mr. Rosenstein in that role appointed special counsel Robert Muller who is on the hot seat here.