Mr. McCabe’s memo, one of several that he wrote, highlights the conflicting roles that Mr. Rosenstein plays in the case. He supervises the special counsel investigation and has told colleagues that protecting it is among his highest priorities. But many current and former law enforcement officials are suspicious of some of his other actions, including allowing some of Mr. Trump’s congressional allies to view crucial documents from the investigation.

Andrew G. McCabe, the former F.B.I. deputy director and a frequent target of President Trump’s scorn, was fired Friday after Attorney General Jeff Sessions rejected an appeal that would have let him retire this weekend.vMr. McCabe promptly declared that his firing, and Mr. Trump’s persistent needling, were intended to undermine the special counsel’s investigation in which he is a potential witness.

A business associate of President Trump promised in 2015 to engineer a real estate deal with the aid of the president of Russia, Vladimir V. Putin, that he said would help Mr. Trump win the presidency.

President Trump told Russian officials in the Oval Office this month that firing the F.B.I. director, James B. Comey, had relieved “great pressure” on him, according to a document summarizing the meeting. The conversation reinforces the notion that President Trump dismissed him primarily because of the bureau’s investigation into possible collusion between his campaign and Russian operatives.