The three-time Emmy Award winner, 63, sat down for breakfast with Halyna's husband Matthew Hutchins and their 9-year-old son Andros on Saturday morning at La Posada in Santa Fe, New Mexico, a source tells PEOPLE.
A noticeably somber Baldwin later bid farewell to Matthew and Andros with a hug. "Honestly, he didn't look good," the insider shares, adding that the group was "definitely sad" during their breakfast.
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"I have spoken with Alec Baldwin and he is being very supportive," Matthew told the Daily Mail on Friday, after Baldwin fired the prop gun that killed Halyna, 42.
"I don't think there are words to communicate the situation," he told Insider on Friday.
"I am not going to be able to comment about the facts or the process of what we're going through right now, but I appreciate that everyone has been very sympathetic," Matthew added. "I think that we will need a little bit of time before we can really encapsulate her life in a way that is easy to communicate."
After PEOPLE confirmed that one crew member died and another was critically injured Thursday on the set of the upcoming Western film, the Santa Fe Sheriff's Department said in a statement that Halyna and writer/director Joel Souza 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 on Thursday. Halyna was airlifted to University of New Mexico Hospital where she died of her injuries. Souza, 48, was released Friday from Christus St. Vincent Regional Medical Center where he underwent treatment for his injuries.
"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 in a statement on Twitter on Friday.
"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," he continued. "My heart is broken for her husband, their son, and all who knew and loved Halyna."
A source also told PEOPLE that Baldwin was "hysterical and absolutely inconsolable for hours," and he's looking "to take some time to himself and re-center himself," as he cancels his other projects.
"This was pretty devastating. This is how he handles difficult times. Whenever something bad happens, in the short term, he removes himself from [the] public eye," the insider said, adding: "Everyone knows this was an accident, but he's absolutely devastated."