Alec Baldwin Speaks Out After Fatal Shooting of Halyna Hutchins on 'Rust' Set: 'She Was My Friend'

Alec Baldwin has spoken out after the fatal shooting incident on the set of his film Rust, which resulted in the death of cinematographer Halyna Hutchins.

The three-time Emmy Award winner, 63, and his wife Hilaria Baldwin spoke to paparazzi on Saturday in Vermont, where their family is "laying low." Although he made it clear that he could not comment on the open investigation, the actor shared some words about Hutchins, 42, in a video shared by TMZ.

"She was my friend, she was my friend," Baldwin said. "The day I arrived in Santa Fe to start shooting, I took her to dinner with Joel [Souza], the director. We were a very, very well-oiled crew shooting a film together, and then this horrible event happened."

He also said he's been in contact with Halyna's husband Matthew Hutchins and their 9-year-old son Andros after they were seen having breakfast together last weekend. "We are in constant contact with him because we're very worried about his family and his kid," Baldwin added. (Matthew previously told the Daily Mail that Alec was "being very supportive" in the wake of Halyna's death.)

On Saturday, Baldwin expressed his support for reforming the use of firearms on movie and TV sets after the incident has prompted Hollywood to take action. "I do know that an ongoing effort to limit the use of firearms on film sets is something I'm extremely interested in," he said.

"That's not for me to decide. It's urgent that you understand I'm not an expert in this field," he said. "So, whatever other people decide is the best way to go in terms of protecting people's safety on film sets, I'm all in favor of and I will cooperate with that in any way that I can."

Saturday's comments marked the first time Baldwin spoke out about the tragic incident in public after he released a statement on Twitter last week.

"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."

After PEOPLE confirmed that one crew member died and another was critically injured last Thursday on the New Mexico set of the upcoming Western film, the Santa Fe Sheriff's Department said in a statement that Halyna and Souza, 48, were "shot when a prop firearm was discharged by Alec Baldwin, producer and actor."

Authorities responded to a 911 call from the Rust set at Bonanza Creek Ranch at around 1:50 p.m. local time. Halyna was airlifted to the University of New Mexico Hospital where she died of her injuries. Souza was released last Friday from Christus St. Vincent Regional Medical Center where he underwent treatment for his injuries.

A source told PEOPLE on Thursday that Alec and Hilaria, 37, were "laying low" with their six children: daughters Carmen Gabriela, 8, and María Lucía Victoria, 7 months, and sons Rafael Thomas, 6, Leonardo Ángel Charles, 5, Romeo Alejandro David, 3, and Eduardo "Edu" Pao Lucas, 13 months.

"Alec and Hilaria left the city and are laying low with the kids," the source said. "They do go out occasionally to pick up dinner, but are mostly trying to protect the kids' privacy and just spend quiet time together as a family."

The source added, "Alec continues to grieve the last week's tragic events, but has found comfort being surrounded by his loved ones. He is trying to focus his attention as best he can on being present for his wife and kids as he works through the trauma. Alec continues to cooperate with the sheriff's office in their investigation."