The actor Alec Baldwin appeared Monday in a Santa Fe courthouse as his lawyers sparred with prosecutors over what evidence could be shown to the jury when he goes on trial this week for the fatal shooting of a cinematographer on the set of the film “Rust.”

Wearing a suit with a gray striped tie and glasses with thick dark frames, Mr. Baldwin, who is facing a charge of involuntary manslaughter, appeared to pay close attention to the proceedings, taking notes and leaning over to speak with a lawyer.

Mr. Baldwin was indicted by a grand jury for his role in the fatal shooting of the cinematographer, Halyna Hutchins, who was killed on Oct. 21, 2021, when a gun he was rehearsing with discharged a live bullet. He has pleaded not guilty, saying he was told the gun did not contain live ammunition. He has also said he did not pull the trigger before the bullet fired, which prosecutors dispute.

The judge in the case, Mary Marlowe Sommer of the First Judicial District in New Mexico, ruled on Monday that prosecutors could not argue that Mr. Baldwin’s role as a member of the production team — he was one of the film’s producers in addition to being its leading man — had made him more culpable for the death of Ms. Hutchins.

“As the producer he has the power to control safety on set, and there was a tremendous lack of safety on this set,” one of the prosecutors, Erlinda O. Johnson, argued in court.

Mr. Baldwin’s defense has disputed that argument, saying that as part of the production team he was involved in creative matters, but that others had authority over hiring and budgets.

The judge ordered that his role as a producer was not relevant to the prosecution, narrowing the trial to Mr. Baldwin’s conduct as an actor who was handed a gun on set that day.

Judge Marlowe Sommer also placed limits on which video evidence could be shown to the jury.

She ruled that jurors could be shown videos that prosecutors believe bolsters their argument that Mr. Baldwin was reckless while handling guns on set. Prosecutors have said that footage shows the actor with his finger on the trigger when it was not required and using his gun as a pointer to direct crew members.

But the judge said the jury could not be shown videos unrelated to Mr. Baldwin handling weapons; prosecutors had sought to admit a video in which he exhorts the crew to work faster.

“Everything else regarding him yelling at the crew or telling people to hurry up — none of that is relevant,” Judge Marlowe Sommer ordered.

The decision was a partial victory for the defense, which has argued that some of the videos the prosecution intended to introduce were aimed at smearing Mr. Baldwin’s character rather than laying out evidence for his conduct on the day of the fatal shooting.

“Mr. Baldwin swore on set — he cussed — and therefore, what, he committed homicide?” Luke Nikas, a lawyer for Mr. Baldwin, said at Monday’s hearing. “Mr. Baldwin’s not a murder on the 21st because he swore on the 16th.”

Jury selection is scheduled for Tuesday, with opening arguments very likely to start on Wednesday.