Photographs published by The Santa Fe New Mexican newspaper - and later by AP - show an emotional Baldwin in tears outside the Santa Fe County Sheriff’s Office.
On Friday it was confirmed Baldwin fired a prop gun on the US set of the Western Rust, killing Hutchins and injuring director Joel Souza.
In a statement posted on his arts foundation’s social media account, Baldwin described the event as a “tragedy” and said he is in communication with Hutchins’s husband.
He said: “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.
“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.”
A number of people voiced their sympathy in wake of the tragedy.
Baldwin’s brother Stephen asked for people’s prayers on his Instagram page.
“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”
Producer Melissa Jo Peltier wrote online: “A tragic accident that chills the heart of anyone who has been around movie set hazards. Peace & comfort to Halyma’s family.”
Actress Nancy Sinatra said: “Alec, you are a dear, kind man who wouldn’t hurt anyone purposefully. I know you will never get over this but please try to remember it was a horrifying accident, a catastrophic tragedy that was not your fault. I’m so terribly sorry for all of you.”
Director Rachel Manson said: “Thank you. She is my friend. Her son is my family. It was not your fault and her final moments I am Certain were spent feeling so happy she was filming you.”
Scores of people also paid tribute to Hutchins on social media.
The camera crew for television series His Dark Materials posted a clapperboard bearing the words RIP Halyna Hutchins on the BBC and HBO programme’s official Twitter page.
“We were devastated to learn of the tragic passing of Halyna Hutchins in the USA,” the post said.
“Our wonderful camera crew created this on set today to pay tribute to ‘one of us’.”
Hollywood star Dwayne Johnson also paid tribute to Hutchins.
The actor, also known as The Rock, commented on Hutchins’ last Instagram post.
Her last post was a video she shared two days ago of herself horse-riding on set and she wrote a “perk” of working on a Western was that “you get to ride horses on your day off”.
Johnson wrote: “I am so so sorry. Rest easy. My love and strength to your family.”