Indeed, Mr. Brennan, who led the C.I.A. under President Barack Obama and has been one of the most vocal intelligence community critics of Mr. Trump, drew attention on Thursday by striking back. He dismissed as “hogwash” the president’s claims of “no collusion” with Russia to influence the 2016 election and argued that Mr. Trump was trying to silence challengers.

“Mr. Trump clearly has become more desperate to protect himself and those close to him, which is why he made the politically motivated decision to revoke my security clearance in an attempt to scare into silence others who might dare to challenge him,” Mr. Brennan wrote in an opinion article in The New York Times. He said the move made it more important than ever for the special counsel in the Russia inquiry, Robert S. Mueller III, to complete his investigation.

But others predicted that political appointees who have security clearances will be nervous about saying or doing anything that might make Mr. Trump angry, especially about the Russia investigation. And it is likely to worry the consulting firms, defense contractors and other private businesses that have employees with security clearances, they said.

“The message he’s sending is: Don’t cross me,” said Mary McCord, who helped run the Justice Department’s national security division until she left last year. “Career national security professionals are good at blocking out the noise of what’s in the news, but it’s harder to ignore when it’s the president attacking you.”

The president’s move to strip former top officials of their ability to access classified information was the latest example of Mr. Trump successfully using the power of his office to exert influence over the political and legal maelstrom swirling around his administration.

He pressured the F.B.I. to fire Andrew G. McCabe, the bureau’s deputy director, and several members of the Mueller team. Mr. Trump helped his allies in Congress to strong-arm the Justice Department to hand over internal documents related to the Russia inquiry. And the president’s repeated attacks on Mr. Mueller’s investigators are meant to undermine the credibility of the investigation in the eyes of the public, lawmakers and even potential jurors.

None of his moves have brought down Mr. Mueller’s investigation, in part because Mr. Trump has mostly resisted the temptation to order officials at the Justice Department to act on his Twitter-fueled musings. And when he has not, including at least two attempts to fire the special counsel, White House aides blocked Mr. Trump’s way.