They also made clear that investigators have been gathering extensive evidence for some time as part of an ongoing grand jury investigation.
The most striking parts of Trump's remarks, though, concerned what he might do about Mueller's investigation.
Before the adjournment, lawyers for Trump and Cohen told a federal judge in NY that they believe some of the documents and devices seized from Cohen during an FBI raid are protected by attorney-client privilege, and they want a chance to review the material before prosecutors get to examine them.
U.S. District Judge Kimba Wood in Manhattan ordered Cohen to appear in court on Monday afternoon, after holding three hearings on Friday into his request for a temporary restraining order (TRO) blocking prosecutors from reviewing seized materials.
Lawyers for President Donald Trump and his personal attorney, Michael Cohen, have told a federal judge in NY that they believe some of the documents and devices seized from Cohen during an FBI raid are protected by attorney-client privilege, and they want a chance to review the material before prosecutors get to examine them.
"It is wise that Mueller and Rosenstein avoided the fatal mistake of Ken Starr when he chose to expand his jurisdiction to the Monica Lewinsky matter, a tawdry subject, but not highly serious to the welfare and security of the American people", William Jeffress, a white-collar defense attorney who worked on the Valerie Plame leak case, told me. McDougal has said she had a longer affair with him. "Many people have said, 'You should fire him, '" Trump said. "I think maybe Trump has met his match in this guy".
Now Trump's long-time lawyer Michael Cohen- who holds secrets about numerous president's personal and financial dealings - is in the crosshairs.
"He certainly believes that he has the power to do so", she said at Tuesday's press briefing.
There were also what one source said were other issues that could be unrelated to Daniels, including smaller investments.
The cover comes after the Federal Bureau of Investigation earlier this week raided Cohen's office, seizing emails, documents and records, some of them related to his payment to adult-film star Stormy Daniels.
Trump's explosive response to news of the raid may help to explain why it was carried out by the U.S. Attorney's Office for the Southern District of NY, rather than by Mueller's team.
"So, I just heard that they broke into the office of one of my personal attorneys-a good man", Trump began, speaking to reporters while on his way into a meeting with military leaders.
Cohen, through his lawyer and in public statements, has denied wrongdoing.
A team at the Department of Justice would need to review any tapes the Federal Bureau of Investigation has seized to determine whether they violate attorney-client privilege and fall within the scope of the search warrants.
The judge said prosecutors believed either a special "taint team" of government lawyers should decide what evidence can be properly viewed by criminal prosecutors. The Enquirer's publisher, American Media Inc., said it paid McDougal for details of the alleged affair, but they never appeared in print. AMI has said she was paid to become a fitness columnist.
Hendon asked for a delay in court proceedings until at least Monday, saying she needed to research the law.
Clifford's lawyer, Michael Avenatti, spoke briefly in court.
"We have every reason to believe that some of the documents seized relate to my client", he said.
The raids enraged Trump, who called them an "attack on the country".
Those confidentiality rules can be set aside under certain circumstances if investigators have evidence that a crime has been committed.
A search warrant used in the raid Monday sought bank records, business records on Cohen's dealing in the taxi industry, information on payments made to a former Playboy model and a porn actress who say they had affairs with Trump, and Cohen's communications with the Trump campaign, according to people familiar with the investigation.
Cohen has said neither the Trump Organization nor the Trump campaign was involved in the transaction with Daniels and he was not reimbursed for the payment.
Trump on Tuesday hunkered down at the White House, cancelling a first trip to Latin America that was due to start on Friday and stewing on a move that could throw America into a constitutional crisis.
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