The comments contrast with President Donald Trump who complained Monday that agents "broke into the office of one of my personal attorneys".
Daniels's lawyer Michael Avenatti later tweeted out that he and his client would "fully cooperate with any search for the truth" relating to the $130,000 payment.
Cohen is under investigation, according to Yahoo News, for "possible bank fraud, wire fraud and campaign finance violations".
Trump, who lashed out on Twitter at Mueller's probe and the Justice Department on Monday evening, met with his lawyers at the White House on Tuesday to discuss the FBI raid, which has confirmed their worst fears - that Mueller's Russian Federation investigation is mushrooming well beyond questions of campaign collusion.
"It's a real disgrace", Trump said.
Geoffrey Berman, the Trump-appointed US Attorney for the Southern District of NY, which had jurisdiction, was recused from the Cohen case and not involved in carrying out the raid.
Before approving a warrant, a judge would have to be persuaded that the lawyer not only has information relevant to the investigation, but that the attorney was an active participant in a crime or was used by his client to commit a crime.
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Trump hit back again late Thursday, instructing trade officials to consider tariffs on an additional $100 billion in imports. That was backed up by Trump's chief economic adviser, Larry Kudlow, who said tariff negotiations with China had not started.
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. Cohen faced public scrutiny for his close ties to Trump earlier this year after a $130,000 payment to adult film actress Stormy Daniels came to light. That's easier said than done, however: he wouldn't be able to do so without approval from Deputy Attorney General Rod Rosenstein, who is believed to be unlikely to be on board with such a move.
Last week, Trump said he did not know about the payment.
"If you go to the attorney's office and you look at attorney-client privileged material by mistake, you're in a world of hurt", Litman said.
Daniels, who initially denied a sexual relationship with the president, is now seeking depositions from both Trump and Cohen.
Asked about the Daniels controversy last week, Trump said he did not know about the payment and declined to comment further, instead referring questions to Cohen. "In other words, I think in many ways what happened with Cohen is less of a potential threat to the attorney-client privilege than what is happening with Cooper". "It's a total witch hunt".
Will Cohen flip? "You just need to break one weak link to do it", Hall said.
Trump circled back and again blamed Attorney General Jeff Sessions, who recused himself from all Russian-related matters because he had worked on Trump's presidential campaign. The White House has consistently said Trump denies the affair. "This is a pure and simple witch hunt". Rosenstein then determines whether to allow Mueller to proceed or to assign the matter to another US attorney or another part of the Justice Department.
Cohen has been a longtime owner of taxi medallions, in addition to working as a top lawyer at the Trump Organization, the paper said.
The raid creates a new legal headache for Trump as he and his attorneys weigh whether to agree to an interview with Mueller's team.