The assistant director of Rust, Dave Halls, had been sacked from a previous production over gun safety violations.
Actor Alec Baldwin accidentally shot dead Halyna Hutchins on the set of the Western last week.
The producers of Freedom’s Path confirmed to press agency AFP on Monday that Halls had been dismissed in 2019.
It came after a crew member “incurred a minor and temporary injury when a gun was unexpectedly discharged”, the statement said.
Rocket Soul Studios said Halls could not be reached for a comment. There is no suggestion that Halls was at fault for the Rust incident.
The studio’s producers said in a statement sent to the BBC: “First of all, our condolences go out to everyone affected by the recent tragic event in New Mexico.
“Halls was removed from set immediately after the prop gun discharged. Production did not resume filming until Dave was off-site. An incident report was taken and filed at that time.”
An affidavit filed over the Rust incident said Halls had handed the gun to Baldwin during a rehearsal and called out “cold gun” as he did so, meaning the weapon had no live ammunition.
“The assistant director (Dave Halls) did not know live rounds were in the prop gun,” the affidavit said.
The description “prop gun” can refer to a range of items, from non-functioning weapons to cap guns. It can also mean a real gun, as in this case.
‘A complicated case’
Speaking on Monday, Juan Rios, spokesman for the Santa Fe Sheriff’s Department which is investigating the incident, described it as “a complicated case”.
He said investigators had interviewed Hannah Gutierrez, who was responsible for the safety of weapons on the set, but gave no further details. Gutierrez has not yet commented publicly and the BBC has been unable to reach her.
An inventory of seized items that was released on Monday also showed that detectives had recovered loose and boxed ammunition from the set, though they would not say which kind.
Investigators hope a forensic analysis of ballistic evidence will shed light on what kind of projectile was fired from the gun and how it got there.
Hutchins was killed and director Joel Souza was injured when a revolver that Baldwin was using during rehearsal discharged.
Baldwin, the director and other members of the cast and crew have also been interviewed. No charges have been brought yet.
Before the incident, camera operators had walked off the set to protest against working conditions.
‘My heart is with Halyna’
In her first public statement about the incident, Baldwin’s wife Hilaria said on Monday that “it’s impossible to express the shock and heartache of such a tragic accident.”
“My heart is with Halyna. Her husband. Her son. Their family and loved ones. And my Alec,” she posted on Instagram.
Elsewhere, a T-shirt which declares: “Guns Don’t Kill People, Alec Baldwin Kills People” is being sold for $27.99 (£20.32) on a merchandise site linked to Donald Trump Jr, the son of the former US President – who Baldwin has routinely mocked on Saturday Night Live.
Many have criticised the T-shirts but Trump Jr has defended the product, tweeting: “Spare me your fake sanctimony.”
Meanwhile, Flint: Who Can You Trust?, an environmental documentary narrated by Baldwin, has been postponed, its director said, following the fatal shooting.