A lawyer for Alec Baldwin says the actor will hand over his mobile phone as part of a probe into the fatal shooting of a cinematographer on the set of the western movie Rust, even as police say he has so far defied their orders to give them the device.

Baldwin’s lawyer, Aaron Dyer, said he had reached a deal with New Mexico authorities to turn in the phone after steps were taken to protect the actor’s privacy in matters unrelated to the Rust investigation.

“Mr Baldwin’s phone is being turned over this week for review,” Mr Dyer said in a statement on Thursday (local time).

“Mr Baldwin has continued to cooperate with the authorities, and any suggestion to the contrary is simply untrue.”

The comments followed a Thursday news release from the Santa Fe County Sheriff’s Office saying Baldwin had failed to comply with a search warrant requesting he hand over the phone and that a New Mexico prosecutor was working with the actor’s lawyer to get it.

“To date, the mobile phone has not been turned over to authorities,” the sheriff’s office said.

The Santa Fe detective leading the Rust investigation obtained the search warrant in December to examine text messages, emails and other information on Baldwin’s mobile phone.

The detective said she requested the warrant as suspects, victims and witnesses “often make and/or receive telephone calls and/or messages before, during and/or after the commission of crime(s)”.

Baldwin has said he was holding a revolver on the film set when it went off during a rehearsal on October 21, firing a live round that killed cinematographer Halyna Hutchins.

In a television interview, Baldwin said he never pulled the trigger and denied responsibility for the shooting.

The New Mexico prosecutor overseeing the case has said some people who handled guns on the set might face criminal charges in connection with Ms Hutchins’ death.

Live rounds as well as blanks and dummies were found on the set after the fatal shooting.

The developments with Baldwin’s mobile phone came as another lawsuit was lodged over the film set tragedy.

It was filed in a New Mexico court by Hannah Gutierrez Reed, the armourer who oversaw firearms, ammunition and related training on the set of the film Rust, along with two colleagues.

It blames ammunition supplier Seth Kenney and his company PDQ Arm & Prop for introducing live rounds to the set where there were supposed to be only blanks and dummies.

Authorities recovered hundreds of rounds of ammunition from the Rust set – a mix of blanks, dummy rounds and what appeared to be live rounds.

“The introduction of live rounds onto the set, which no one anticipated, combined with the rushed and chaotic atmosphere, created a perfect storm for a safety incident,” the lawsuit states.

Mr Kenney could not be reached for comment. He has said previously that he was sure his company did not send any live rounds to the Rust set.

The lawsuit adds new details to the chain of custody for guns and ammunition on the set on October 21, describing the appearance of a new box of ammunition – presumed to be harmless dummy rounds with no explosive – shortly before a revolver was loaded and passed to Baldwin.

The new lawsuit seeks damages at a jury trial on allegations of unfair trade practices, introducing dangerous products, and false labels and misrepresentation.

It states that authorities found on set “a suspected seven live rounds distributed inside the ammo box, on the ammo cart and in the bandoliers.”

The lawsuit also accuses Mr Kenney of inserting himself in the investigations and attempting to implicate Gutierrez Reed.

-with AAP