Mr. Trump has weighed aloud in recent days to close associates whether to dismiss his lawyer Ty Cobb, who had pushed most strongly a strategy of cooperating fully with the special counsel investigation. The president reassured Mr. Cobb that he had no plans to fire him, according to a person who spoke with the president late Monday, in part to prevent a narrative that his team was in disarray after The New York Times began making inquiries.

Mr. Trump’s lead lawyer, John Dowd, has contemplated leaving his post because he has concluded that he has no control over the behavior of the president, the two people briefed on the matter said. Ignoring his lawyers’ advice, Mr. Trump has reverted to a more aggressive strategy of publicly assailing the inquiry that he initially adopted in the weeks immediately after the special counsel, Robert S. Mueller III, was appointed. Now the president has begun attacking Mr. Mueller himself.

The shift in tone appears to be a product of the president’s concern that the investigation into possible ties between his associates and Russia’s election interference is bearing down on him more directly.