Santa Fe, New Mexico - Alec Baldwin has shared a social media post from a crew member of Rust dismissing concerns about safety on the set of the film.

The Hollywood actor accidentally shot and killed cinematographer Halyna Hutchins when a gun he was holding went off during filming in New Mexico last month.

A police investigation is under way into the shooting, which also left Rust director Joel Souza injured.

Authorities in Santa Fe are probing how a suspected live round came to be in the firearm, which had been declared safe by an assistant director, according to court documents.

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Following the shooting, reports emerged of concerns about safety on the set and the Santa Fe county sheriff said there had been "some complacency" in how weapons were handled.

However, costume designer Terese Magpale Davis, who said she worked on the film, wrote on social media "the story being spun of us being overworked and surrounded by unsafe, chaotic conditions is bullshit."

The post, shared by Baldwin (63) on Instagram along with the caption "read this," defended conditions on set following complaints from crew members.

"These producers who supposedly don't care about their crew have worked tirelessly alongside us," the post said.

Baldwin is a producer on Rust as well as being the star.

Davis defended the film's weapons expert, armorer Hannah Gutierrez Reed, who handed the gun to assistant director David Halls before he gave it to Baldwin.

She said: "The armorer had apprenticed to a well known armorer and had been in the same position on the same type of movie a few months before."

Addressing reports of misfires on the set before the fatal incident, Davis said they were "accidental discharges, which are more common than you think."

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Davis said the crew sometimes had multiple safety meetings per day, and defended Halls while calling for greater awareness of guns on set.

"This is about gun safety," she wrote. "Something we could all stand to learn a little more about so that we know if we're seeing something a bit off."

"I know that's not as much fun to jump on as vilifying producers. Personal responsibility is the last thing anyone wants to focus on in a tragedy."

She then appeared to delete the lengthy Facebook post, but by that time, Baldwin had already shared screenshots of it on his Instagram account.

The star spoke publicly about the shooting over the weekend and paid tribute to rising star cinematographer Hutchins (42).

"She was my friend," Baldwin told photographers in Vermont.

"We were a very, very well-oiled crew shooting a film together and then this horrible event happened."

Baldwin, whose film roles include The Hunt for Red October and Glengarry Glen Ross, called the shooting a "one-in-a-trillion event."

Production on Rust has been halted indefinitely while authorities investigate the shooting. Prosecutors said it is too early to tell if criminal charges will be brought in the case.