The shot hit cinematographer Halyna Hutchins in the chest, according to the Santa Fe County Sheriff's Office. She died of her wounds and Souza, who was behind her, was injured but later released from the hospital.
Souza did not give details of the accident or his injuries but said he was "humbled and grateful by the outpouring of affection we have received from our filmmaking community, the people of Santa Fe, and the hundreds of strangers who have reached out."
On Friday a Santa Fe judge approved a warrant for the sheriff's office to seize firearms, clothing, cameras, video tapes and ammunition from the Bonanza Creek Ranch outside Santa Fe, where Baldwin was filming the low budget Western "Rust"
Security guards were posted at the road leading to the ranch on Saturday.
According to an affidavit filed by a sheriff's office detective, Baldwin was handed what he believed was a safe or "cold" prop gun during a rehearsal on Thursday, but it contained live rounds when it was fired.
No charges have been filed in the case.
The crew member, or armorer, who handled weapons on the set was identified by U.S. media as a 24-year-old woman, who spoke on a podcast earlier this year about learning the job from her veteran father but who only recently worked on her first film as head armorer. The woman could not be reached for comment on Saturday.
The International Cinematographers Guild planned to hold a candlelight vigil for Hutchins, 42, on Saturday evening in Albuquerque, about 40 miles (64 km) from the ranch. A second vigil was scheduled for Sunday in the Los Angeles area.
"Halyna inspired us all with her passion and vision, and her legacy is too meaningful to encapsulate in words. Our loss is enormous," her husband Matt Hutchins wrote on Twitter.
The American Film Institute set up a scholarship fund for female cinematographers in Hutchins' honor.
Baldwin, 63, best known for his roles in TV comedy "30 Rock" and his "Saturday Night Live" impersonations of former U.S. President Donald Trump, said on Friday he was shocked and heartbroken at Hutchins' death and was fully cooperating with authorities.
According to multiple media reports and accounts on social media, some of the crew on "Rust" had walked off the job citing concerns about safety prior to Thursday's shooting.
"We cited everything from lack of payment for three weeks, taking our hotels away despite asking for them in our deals, lack of Covid safety, and on top of that, poor gun safety! Poor on-set safety period!" one camera crew member wrote on a private Facebook page, according to Hollywood publication Deadline.com
Rust Movie Productions said in a statement on Friday it was investigating the incident.
"Though we were not made aware of any official complaints concerning weapon or prop safety on set, we will be conducting an internal review of our procedures while production is shut down," the company said.
(Reporting by Lisa Richwine; Writing by Jill Serjeant; Editing by Daniel Wallis) ((firstname.lastname@example.org; 310 491 7279;))