The police investigation into a fatal shooting with a prop gun fired by actor Alec Baldwin on a film set was focusing on the specialist in charge of the weapon and the assistant director who handed it to Mr Baldwin.

Ukraine-born cinematographer Halyna Hutchins, 42, was struck in the chest and died shortly after the incident on Thursday in New Mexico, while director Joel Souza, 48, who was standing behind her as they lined up a shot, was wounded and hospitalised before being released.

Police interviewed Mr Baldwin, who willingly cooperated, but have pressed no charges.

The incident stunned many in Hollywood and beyond, sparking intense speculation about how such an accident, on the set of a 19th-century western called 'Rust', could have occurred despite elaborate gun-safety protocols for film sets.

The gun, which was supposed to be loaded with a blank charge, instead had a live round, according to the affidavit submitted by the Santa Fe County sheriff's office to obtain a search warrant.

It said that Assistant Director Dave Halls, identified as the man who handed the gun to Mr Baldwin during a rehearsal, called out "cold gun" as he did so - industry code to indicate the weapon had only a blank charge.

"The Assistant Director (Dave Halls) did not know live rounds were in the prop-gun" when he gave it to Mr Baldwin, the affidavit said.

It said police wanted to determine whether any video footage or mobile phone images would shed light on the incident; to check the "western style" outfit worn by Mr Baldwin; and to check all firearms, ammunition and casings on the scene.

It said that Mr Baldwin handed the gun to 24-year-old Hannah Gutierrez-Reed - the movie's weapons master, or armorer - immediately after the shooting, and that she removed a spent casing and handed both to deputies when they arrived.

Detailed gun safety guidelines from the Actors' Equity Association group specify that "all loading of firearms must be done by the property master, armorer or experienced persons working under their direct supervision".

The guidelines also state: "Before each use, make sure the gun has been test-fired off stage and then ask to test fire it yourself. Watch the prop master check the cylinders and barrel to be sure no foreign object or dummy bullet has become lodged inside."

Santa Fe Sheriff's Department Detective Joel Cano said the incident took place during a rehearsal and it was not clear whether it had been filmed.

He said the prop gun was one of three on a cart outside a building. One of them was taken by the assistant director on the film who went inside and handed it to Mr Baldwin.

"As the assistant director handed the gun to the actor Alec Baldwin, (he) yelled 'cold gun', indicating the prop gun did not have any live rounds," the affidavit said.

District Attorney Mary Carmack-Altwies said in a statement yesterday that the case is in its preliminary stages, adding, "At this time, we do not know if charges will be filed".

The Los Angeles Times, citing anonymous sources, reported that there had been at least three prop gun misfires prior to the fatal accident, and some crew members had protested that and other working conditions.

It said at least one camera operator had messaged a production manager, saying, "We've now had three accidental discharges. This is super unsafe."

Rust Movie Productions said in a statement that it had not been made aware of any "official complaints" but would "continue to cooperate with the Santa Fe authorities".

It said it was also conducting an internal review.

'Rust', for which Mr Baldwin is a co-producer, was being filmed in the foothills of northern New Mexico on sprawling Bonanza Creek Ranch, which has been used as the setting for scores of films.

Read more: Guns on film: How are they used safely?

The International Alliance of Theatrical Stage Employees (IATSE) said in a statement that it was devastated to learn of the death of Ms Hutchins, who was a member of the union.

Ms Hutchins' representatives in a statement said they "hope this tragedy will reveal new lessons for how to better ensure safety for every crew member on set".

Ms Hutchins, 42, who was originally from Ukraine, was named one of American Cinematographer's Rising Stars of 2019.

Her last social media post, two days ago, shows her smiling under a wide-brimmed hat as she rides a horse. "One of the perks of shooting a western is you get to ride horses on your day off :)" she captioned the video.

Known for his impersonations of former US President Donald Trump on sketch show 'Saturday Night Live,' Mr Baldwin has appeared in more than 100 TV and film comedies and dramas, and won Emmy awards for his role as an egotistical TV network executive in the satire '30 Rock'.

The accident renewed debate about whether certain types of prop guns should be banned on TV and film sets.

Brandon Lee, son of martial arts legend Bruce Lee, died at age 28 after being fatally wounded in 1993 by a prop gun in an on-set accident while filming 'The Crow'.

"I don't understand why we would still use blank rounds in a day when you could simulate them," indie film director and producer Ben Rock said.