But the president has wide latitude on clearances, and courts are reluctant to overrule presidents on national security matters, Mr. Smith said, so there is probably little the former officials can do to block the move if the White House moves forward.

Mr. Clapper declined to discuss the threat in detail but repeated comments he first made in an interview on CNN: “This is just a very, very petty thing to do. And that’s about all I’ll say about it.”

Another former official being targeted, Michael V. Hayden, the former head of the C.I.A. and National Security Agency during the George W. Bush administration and a principal at the Chertoff Group who just wrote a book, said the removal of his security clearance would not affect “what I say or write.” He added on Twitter that he does not go to the White House for classified briefings.

As unusual as the suggestion was, it reflected an equally remarkable dynamic that has taken hold in the Trump era: the fact that so many former senior intelligence officials are willing to regularly criticize the sitting president in public.

Senior intelligence officials generally consider themselves, and the information they provide, nonpartisan. During past administrations, they have attempted to maintain an apolitical posture once they left the government, limiting their public criticism of successors.

But Mr. Trump has routinely attacked intelligence agencies, portraying them as part of a so-called deep state, an unelected cabal seeking to steer United States policy and undercut him. Last year after a meeting with Mr. Putin, Mr. Trump called Mr. Brennan, Mr. Clapper and Mr. Comey “political hacks” as he cast doubt on Russia’s interference.

After Mr. Trump again stood alongside President Vladimir V. Putin of Russia in Finland last week and sided with him over the intelligence community to cast doubt about the campaign meddling, the trio renewed their denunciations.