In an email obtained by PEOPLE that was sent to crew members on Sunday night, the movie's production team wrote they "have made the decision to wrap the set at least until the investigations are complete."
"Although our hearts are broken, and it is hard to see beyond the horizon, this is, at the moment, a pause rather than an end," the email read. "The spirit that brought us all to this special place remains."
Authorities in New Mexico are currently investigating the death of Hutchins, who died after being airlifted to the University of New Mexico Hospital on Thursday. Baldwin, 63, shot a prop firearm while rehearsing a scene on the set of the movie and killed Hutchins. Director Joel Souza was also injured in the incident but was released from the hospital the following day.
The production team included in its email that they would be matching any donations made by the Rust crew to the Halyna Hutchins Scholarship Fund, which was created by her family.
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On Friday, Baldwin spoke about the incident on Twitter, writing, "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."
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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."
"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," added Matthew, who has an 8-year-old son he shared with the late cinematographer. "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."