The federal judge overseeing former President Donald J. Trump’s classified documents case showed little patience on Tuesday with an argument by his lawyers that the F.B.I.’s search two years ago of Mar-a-Lago, his private club and residence in Florida, was conducted improperly.

The judge, Aileen M. Cannon, has granted a serious audience to several far-fetched arguments by Mr. Trump’s lawyers. But the skepticism she displayed toward their position at a hearing in Federal District Court in Fort Pierce, Fla., was a rare example of her turning a critical eye on the defense.

At the hearing, Mr. Trump’s legal team had asked Judge Cannon to suppress any evidence collected during the Mar-a-Lago search — including most of the 32 classified documents he has been charged with removing from the White House — because, they said, the warrant was not specific enough about which parts of the property the F.B.I. could search and what items it could seize.

“It seems like it is,” Judge Cannon said, disagreeing with Mr. Trump’s lawyers about the question of specificity and all but ruling against them from the bench. “I have a hard time seeing what other language needed to be included.”

Granting the defense’s request would be a deadly blow to the classified documents case, keeping the jury from seeing the highly sensitive national security files that Mr. Trump has been accused of holding on to after he left office.

The search of Mar-a-Lago, which took place on Aug. 8, 2022, is the central investigative step in the extraordinary criminal inquiry into Mr. Trump’s handling of classified materials and attempts to obstruct the government’s efforts to retrieve them.