Alec Baldwin.Photo: Mark Sagliocco/Getty

Alec Baldwin attends the World Premiere of National Geographic Documentary Films' ‘The First Wave’ at Hamptons International Film Festival on October 07, 2021 in East Hampton, New York.

Alec Baldwin"is canceling other projects" following anaccidental shootingon the set of his film,Rust,that left cinematographerHalyna Hutchinsdead and directorJoel Souzainjured.

A source tells PEOPLE that Baldwin, 63, is looking “to take some time to himself and re-center himself,” as he has during difficult times in the past.

“This was pretty devastating,” the source says. “This is how he handles difficult times. Whenever something bad happens, in the short term, he removes himself from [the] public eye.”

The source confirms to PEOPLE that Baldwin was “hysterical and absolutely inconsolable for hours” following the shooting: “Everyone knows this was an accident, but he’s absolutely devastated.

For more on the shooting on theRustset, listen below toour daily podcast PEOPLE Every Day.

Alec Baldwin; Halyna Hutchins.Jim Spellman/Getty; Fred Hayes/Getty

Alec Baldwin - Halyna Hutchins

Hutchins was airlifted to the University of New Mexico Hospital where she died from her injuries, according to the sheriff’s department. Souza was hospitalized, but his reps toldDeadlinehe has since been released.

“[Baldwin] is someone who really deeply cares, so he can be very hard on himself,” the source shares. “That’s true in general, in situations nowhere near as serious as this. But in this situation, it’s a whole other level because of the loss of life involved.”

“It’s going to take him time to figure all this out,” they add. “He needs to take a while to himself, to be with his family.”

So far, no charges have been filed and an investigation remains ongoing.

In the wake of the tragedy, a source previously told PEOPLE that “Alec isstill trying to get his head around everythingthat happened. This has been devastating. It’s been incredibly difficult.”

Baldwin firstspoke outregarding the incident on Friday morning, issuing a two-part statement on Twitter.

“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,” the actor began.

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“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.”

Hutchins' husband Matthew, with whom she shares 9-year-old son Andros,has since been in contact with Baldwin. “I have spoken with Alec Baldwin and he is being very supportive,” Matthew told theDaily Mail.

TheRustfilm set has been shut down following Hutchins' death, with production indefinitely paused, according to the production company, Rust Movie Productions, LLC.

source: people.com