THE TIGHTENING NOOSE:

Rod J. Rosenstein, the veteran Republican prosecutor handpicked by Mr. Trump to serve as deputy attorney general, personally signed off on Monday's F.B.I. decision to raid the office of Mr. Cohen, a longtime confidant of Mr. Trump, several government officials said.

The early-morning searches enraged Mr. Trump, associates said, setting off a public tirade Monday evening that continued in private at the White House as the president fumed about whether he should fire Mr. Rosenstein.

As Mr. Trump has stewed over the developments, he has cast blame in many directions. Publicly, he has expressed frustration with his attorney general and deputy attorney general. Privately, people close to the president said, he has also blamed Mr. Cohen for publicly acknowledging the payments to Ms. Clifford.

The episode has deeply unsettled White House aides, Justice Department officials and lawmakers from both parties, who believe the president may use it as a pretext to purge the team leading the investigation into Russia's meddling in the 2016 election.

Searching a lawyer's files is among the most sensitive moves federal prosecutors can make as they pursue a criminal investigation. Mr. Rosenstein's personal involvement in the decision signals that the evidence seen by law enforcement officials was significant enough to convince the Justice Department's second in command that such an aggressive move was necessary.

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