By Agence France-Presse
Agents seized files relating to Cohen's work, which included making a $130,000 payment before the 2016 election to an adult film actress who says she had a tryst with the Trump.
Cohen's own attorney Stephen Ryan said agents were working in part on the request of Mueller, the independent prosecutor investigating links between Russia and the Trump campaign.
At the White House, Trump angrily denounced the raid on Cohen, whom he called "a good man."
"It's a disgraceful situation. It's a total witch-hunt, I have been saying it for a long time," he told reporters.
"It's an attack on our country in a true sense. It's an attack on what we all stand for," he said.
The raid came as Mueller's probe intensifies its focus on Trump's inner circle. Mueller's team is examining possible collusion between Trump's campaign and Moscow, allegations of corrupt behavior by Trump campaign lieutenants, and of White House efforts to obstruct the investigation.
So far 19 people have been indicted, including the chairman of Trump's campaign and his former national security advisor.
Trump accused Mueller Monday of overseeing a biased investigation staffed by Democrats, "a pure and simple witch-hunt."
- Trump attacks Mueller -
After having turned over what he called a million pages of documents, Trump said the investigation is "now getting ridiculous. They found no collusion whatsoever with Russia."
"This is the most biased group of people, these people have the biggest conflicts of interest I've ever seen. Democrats all, or just about all."
Asked if he wants to fire Mueller, Trump replied: "Many people have said you should fire him. Again they found nothing and in finding nothing that's a big statement," he said. "So we'll see what happens."
The veteran prosecutor, a former FBI director, is seeking to interview Trump, but has not said the president is a target in the investigation.
The raid on Cohen though takes the probe close to the Oval Office. Cohen has been Trump's personal lawyer and confidant for years, helping him on real estate and personal matters, as well as informally advising him since he became president.
He is also known as a rough-and-tumble "fixer" for Trump, dedicated to protecting his boss's interests.
- Raid tied to alleged affair -
US media said documents seized in the raid related to the surreptitious payment Cohen made to porn actress Stormy Daniels that, according to Daniels, aimed to keep her quiet about her earlier relationship with Trump.
The Washington Post reported that Cohen is under examination for possible bank fraud and campaign finance violations.
Daniels, whose real name is Stephanie Clifford, is one of several women who claim to have had affairs with Trump in the past and were pressured or paid to keep quiet about them.
Last month Daniels told 21 million TV watchers that she had unprotected sex with Trump after meeting with him at a celebrity golf tournament in Lake Tahoe, California in July 2006. That was shortly after Trump's wife Melania gave birth to their son.
Trump has skirted questions about the relationship, and last week denied any knowledge of Cohen's $130,000 payment, which was made to secure Daniels's signature in October 2016 on a secret agreement to not talk about the affair.
But since then media reports have made it public, and last month she sued in a California court to have the hush deal annulled. Cohen countersued, demanding some $20 million in penalties for her violating the non-disclosure pact.
Cohen has said that neither the Trump Organization, the president's real estate group, nor the Trump campaign was a party to the transaction with Daniels.
"Neither reimbursed me for the payment, either directly or indirectly," Cohen said.
After the raid Monday, Cohen's attorney Ryan accused prosecutors of seizing privileged communications between Cohen and his clients.
"The decision by the US attorney's office in New York to conduct their investigation using search warrants is completely inappropriate and unnecessary," Ryan said.
"It resulted in the unnecessary seizure of protected attorney-client communications between a lawyer and his clients."