Aileen M. Cannon, the federal judge overseeing the prosecution of a man accused of trying to assassinate former President Donald J. Trump, rejected the man’s request that she remove herself from the case, saying on Tuesday that she has no relationship with Mr. Trump even though he appointed her to the bench and she has ruled in his favor in a separate criminal matter.

Judge Cannon denied the request by the defendant, Ryan W. Routh, in a brief decision issued in Federal District Court in Fort Pierce, Fla. Mr. Routh was arrested last month in West Palm Beach after Secret Service agents spotted him carrying a rifle in the bushes along the fence line of one of Mr. Trump’s golf courses.

Mr. Routh’s lawyers first asked Judge Cannon to remove herself from the case two weeks ago. In their initial request, they argued that Mr. Trump had “repeatedly praised” her rulings in a separate case in which he stood accused of illegally holding onto classified documents after he left office.

In an unexpected decision in that matter, Judge Cannon threw out all the charges against Mr. Trump in July, ruling against decades of legal precedent that Jack Smith, the special counsel who filed the indictment, had been illegally appointed to his job.

But in her decision on Tuesday, Judge Cannon rebuffed the idea that she had been affected by Mr. Trump’s praise. She said she had in fact never met or spoken to the former president except “in connection with his required presence” in her courtroom for hearings in the classified documents case.

“I have no control over what private citizens, members of the media, or public officials or candidates elect to say about me or my judicial rulings,” Judge Cannon wrote. “Nor am I concerned about the political consequences of my rulings or how those rulings might be viewed by ‘some in the media.’”