White House press secretary Sarah Huckabee Sanders on Tuesday said President Trump has the power to fire special counsel Robert Mueller as Democrats demanded legislative protections for Mr. Mueller and the team investigating the Russian meddling probe.

Legal experts have debated whether Mr. Trump has the authority to directly fire Mr. Mueller. Under Justice Department guidelines, a special counsel can only be fired by the official in charge of the investigation, which would be Deputy Attorney General Rod Rosenstein.

“We’ve been advised that the president certainly has the power to make that decision,” Mrs. Sanders said. But she added that the president is not moving in that direction now.

Senate Democrats, meanwhile, demanded legislation to protect Mr. Mueller from being fired by the president.

Minority Leader Charles E. Schumer, New York Democrat, warned that Mr. Mueller’s firing could create a constitutional crisis. He said that some of the bills have bipartisan support and called upon Majority Leader Mitch McConnell, Kentucky Republican, to bring the legislation to the floor “very soon.”

Mr. Trump on Monday hinted that he is considering terminating the special counsel, who he says has strayed widely from its mission to investigate collusion between Russia and the Trump campaign before the 2016 election.

“Why don’t I just fire Mueller? Well, I think it’s a disgrace what’s going on. We’ll see what happens,” Mr. Trump said in the wake of raids on his personal attorney’s office, house and hotel room. “But I think it’s really a sad situation, when you look at what happened. And many people have said, you should fire him.”

The investigation into Mr. Trump’s personal attorney Michael Cohen is focusing on payments allegedly made to silence women who claimed to have had affairs with the president more than a decade ago.

FBI agents Monday searched Mr. Cohen’s office, house and a hotel where he was staying while his home is under renovation. They seized thousands of documents, including tax records, business papers and emails between Mr. Trump and Mr. Cohen.

The raid was said to be focused on records related to the $130,000 payment to adult film actress Stormy Daniels. Agents were also said to be seeking documents detailing an agreement between ex-Playboy Playmate Karen McDougal and a media company that allegedly paid her for her story.

Ms. McDougal has claimed The National Enquirer paid her $150,000 for her story, but then spiked the article. Last month, Ms. McDougal filed a lawsuit against American Media Inc. seeking to be released from the deal.

Both women were reportedly paid just before the 2016 election.

Mr. Trump told reports last week he was unaware of the payment to Ms. Clifford or the source of the funds.

“You’ll have to ask Michael Cohen,” the president told reports on Air Force One. “Michael is my attorney. You’ll have to ask Michael.”

FBI agents also searched for information unrelated to Ms. Daniels or Ms. McDougal, including investments held by Mr. Cohen, including his ownership of two taxi medallions. The medallions are essentially a license to own a taxi cab and are extremely valuable in New York.

The search was said to be personally green lighted by Mr. Rosenstein based on a referral from Mr. Mueller.

In a separate development, Geoffrey Berman, the U.S. Attorney for the Southern District of New York, has recused himself from the Cohen investigation. Mr, Rosenstein was said to have approved Mr. Berman’s recusal.

Mr. Berman, a Trump appointee, donated $5,400 to the president’s 2016 campaign, The New York Times reported in 2017. He volunteered for Mr. Trump’s New Jersey campaign operation and was once a law partner with former New York City Mayor Rudy Giuliani, one of the president’s top advocates during the election.

A spokesman for the U.S. Attorney’s Office for the Southern District of New York declined to comment.

Mr. Berman has served as the interim U.S. attorney since January, after Mr. Trump fired the previous U.S. attorney, Preet Bharara. A federal prosecutor for 30 years, Mr. Berman will remain an interim U.S. attorney until he is confirmed by the Senate. It is not known when a confirmation hearing will occur and one has not been scheduled.

Mr. Bharara, who was fired in January by Mr. Trump, said in a Tuesday afternoon tweet that Mr. Berman’s recusal “makes sense.”

Later Tuesday, newly filed court documents show that Mr. Mueller is seeking information about possible criminal activity by Paul Manafort while he was chairman of Mr. Trump’s presidential campaign.

The documents included a heavily redacted search warrant application used by Mr. Mueller. It revealed that prosecutors were interested in possible campaign finance law violations during a June 2016 meeting between Aras and Emin Agalarov, a Russian billionaire and his son, and Mr. Manafort, Donald Trump Jr. and Jared Kushner.

The search warrant details were disclosed in a motion to suppress evidence seized in a July 2017 raid on Mr. Manafort’s Alexandria, Virginia, home.

Mr. Manafort’s attorney claims the seizure of computers and electronic devices was “overly broad,” saying some of the devices may not have been used in the alleged crimes. For example, investigators seized an Apple iPod Touch sitting in a junk drawer, according to motion.

The motion also asks the judge to return evidence collected during the raid, claiming it was a Fourth Amendment violation.

Mr. Manafort faces tax evasion and money laundering charges in Washington, D.C., and Virginia. He has pleaded innocent in both cases.

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