"There are no words to convey my shock and sadness regarding the tragic accident that took the life of Halyna Hutchins, a wife, mother and deeply admired colleague of ours," Baldwin wrote. "I'm fully cooperating with the police investigation to address how this tragedy occurred and I am in touch with her husband, offering my support to him and his family."
"My heart is broken for her husband, their son, and all who knew and loved Halyna," he added.
Baldwin's statement comes shortly after his brother, Stephen Baldwin, took to Instagram to address the fatal incident.
"Asking for your prayers tonight friends not much can be said other than please pray for all involved in the wake of this tragic accident thank you," the younger Baldwin wrote.
Hutchins, 42, was transported by helicopter to University of New Mexico Hospital in Albuquerque after the incident, the Santa Fe Sheriff’s Department previously confirmed to ET. She was pronounced dead by medical personnel at the hospital.
Souza, meanwhile, was transported by ambulance to Christus St. Vincent Regional Medical center in Santa Fe, and has since been released.
It's unclear how the incident occurred or the circumstances surrounding the discharging of the prop gun.
Baldwin was reportedly questioned by investigators on Thursday at the Sheriff's Department, according to the Santa Fe New Mexican. The actor was also photographed outside the sheriff's department after answering questions, and reportedly was in tears as he spoke with someone on the phone.
"This investigation remains open and active," the Sheriff’s Department told ET. "No charges have been filed in regard to this incident. Witnesses continue to be interviewed by detectives."
Cinematographers Guild National President John Lindley and National Executive Director Rebecca Rhine released a statement to ET regarding the tragedy.
"We received the devastating news this evening, that one of our members, Halyna Hutchins, the Director of Photography on a production called Rust in New Mexico died from injuries sustained on the set," they said. "The details are unclear at this moment, but we are working to learn more, and we support a full investigation into this tragic event. This is a terrible loss, and we mourn the passing of a member of our Guild’s family."
As for the film itself, Rust is a Western about a 13-year-old boy left to fend for himself and his younger brother following the death of their parents in 1880s Kansas. The boy is forced to go on the run with his long estranged grandfather after he's sentenced to hang for the accidental killing of a local rancher.