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 persuade the Justice Department’s second-in-command that such an aggressive move was necessary.
Mr. Trump’s advisers have spent the last 24 hours trying to convince the president not to make an impulsive decision that could put the president in more legal jeopardy and ignite a controversy that could consume his presidency, several people close to Mr. Trump said. The president began Tuesday morning with a pair of angry tweets, calling the raids “A TOTAL WITCH HUNT!” and venting that “attorney–client privilege is dead!”
Mr. Trump has long been mistrustful of Mr. Rosenstein, the Justice Department’s No. 2 official, who appointed the special counsel, Robert S. Mueller III, and now oversees his investigation into Mr. Trump’s campaign and possible obstruction of justice by the president. In his remarks Monday night, the president lashed out at Mr. Rosenstein for having “signed a FISA warrant,” apparently a reference to the role Mr. Rosenstein played in authorizing the wiretap of a Trump associate in the Russia inquiry.
Mr. Trump considered firing Mr. Rosenstein last summer. Instead, he ordered Mr. Mueller to be fired, then backed down after the White House counsel refused to carry out the order, The New York Times reported in January. Mr. Trump is now again telling associates that he is frustrated with Mr. Rosenstein, according to one official familiar with the conversations.
While Mr. Rosenstein must sign off on all moves that Mr. Mueller makes, that is not necessarily the case for searches — like this one — that are carried out by other federal law enforcement offices. Justice Department regulations require prosecutors to consult with senior criminal prosecutors in Washington — but not necessarily the deputy attorney general — before conducting a search of a lawyer’s files.
The involvement of Mr. Rosenstein and top prosecutors in New York in the raid of Mr. Cohen’s office makes it harder for Mr. Trump to argue that his legal problems are the result of a witch hunt led by Mr. Mueller. In addition to Mr. Rosenstein, all of the top law enforcement officials involved in the raid are Republicans: Mr. Mueller, Christopher A. Wray, the F.B.I. Director, and Geoffrey Berman, the interim United States attorney in New York.
While Mr. Trump is focused for the moment on Mr. Rosenstein, many of the president’s advisers and allies are fearful that the president also intends to fire Mr. Mueller in an attempt to end the Russia investigation. Asked by reporters on Monday night whether he intends to do so, Mr. Trump said, “We’ll see what happens.”
“But I think it’s really a sad situation when you look at what happened,” the president added. “And many people have said you should fire him. Again, they found nothing and in finding nothing, that’s a big statement.”
The prospect that Mr. Trump might fire Mr. Mueller was met with fierce responses from Democrats and some Republicans, who warned that such a move would be disastrous for the White House.
Senator Charles E. Grassley of Iowa, the Republican chairman of the Judiciary Committee, said Tuesday on Fox Business Network that “it would be suicide for the president to want to talk about firing Mueller.”
Representative Nancy Pelosi of California, the top Democrat in the House, on Monday called Mr. Trump’s attacks on Mr. Mueller and his team a “grave reminder of his utter contempt for the rule of law.”
The president has for months been harshly critical of Attorney General Jeff Sessions for having recused himself in the Russia investigation. Mr. Trump renewed that criticism Monday night, saying that “he made what I consider to be a very terrible mistake for the country, but you’ll figure that out.”
As the president’s attacks became more severe over the past months, top Justice Department officials quietly worried about what to do should Mr. Trump fire the special counsel or one of his top officials. They chose to band together in a public show of solidarity in late February, when Mr. Sessions dined with Mr. Rosenstein, the deputy attorney general who is overseeing Mr. Mueller, and Noel J. Francisco, the solicitor general who would oversee the Russia investigation should Mr. Rosenstein be fired.