The federal judge overseeing former President Donald J. Trump’s prosecution on charges of mishandling classified documents expressed deep reservations on Thursday about some of the motions filed by his lawyers seeking to have the case dismissed.

At a nearly daylong hearing in Federal District Court in Fort Pierce, Fla., the judge, Aileen M. Cannon, entertained arguments from the lawyers and from prosecutors in the office of the special counsel Jack Smith about two of the former president’s more unorthodox attacks on the federal indictment.

One of those attacks by Mr. Trump’s team was a direct, albeit dubious, assault on the constitutionality of the Espionage Act, which the government says Mr. Trump violated 32 times by removing a trove of highly sensitive classified material from the White House after he left office.

In the other attack, Mr. Trump’s lawyers asserted that under a law known as the Presidential Records Act, Mr. Trump designated the documents he took with him as his own personal property and so he could not be charged with possessing them without authorization.

But Judge Cannon, who was appointed by Mr. Trump near the end of his term, seemed skeptical about both of the claims. As Mr. Trump and Mr. Smith sat in front of her on opposite sides of the courtroom, she said it would be an “extraordinary” move for a judge to unilaterally strike down the Espionage Act, the chief federal law governing the handling of classified material.

She also said that while Mr. Trump was free to claim at trial that the documents he was charged with holding actually belonged to him, it was “difficult to see” how that argument warranted tossing the entire case out before it went to a jury.