Ireland Baldwin shared a message of support for father Alec as prosecutors said it was too early to tell if criminal charges would be brought in the shooting death of a cinematographer.
An investigation is under way into the tragedy, with new details emerging from the incident including confirmation the bullet thought to have ended the life of Hutchins has been recovered.
Santa Fe district attorney Mary Carmack-Altwies did not rule out bringing charges against Baldwin and said "all options are on the table at this point".
Ireland, Baldwin’s daughter from his marriage to actress Kim Basinger, has shared another message of support for her father.
She posted a comment from a fan who said they had once taken care of an on-set rider for Baldwin in the 1990s and his only request was for milk and cereal for his then young daughter.
Ireland, a 26-year-old model, wrote alongside the post: "Amongst some of the most abhorrent and threatening comments, emails, text messages, and voicemails I’ve been getting... this beautiful comment stands alone. I know my dad, you simply don’t. I love you, Dad."
Hutchins, a 42-year-old rising star in the film industry, was killed on October 21 on the set of Rust at Bonanza Creek Ranch in Santa Fe.
Director Joel Souza was also injured, though he is now recovering after leaving hospital.
How the shooting occurred has been the subject of intense speculation.
Two people handled the revolver, described by Carmack-Altwies as an "antique era-appropriate gun", before it was given to Baldwin, Santa Fe county sheriff Adan Mendoza said.
They were armourer Hannah Gutierrez-Reed and assistant director David Halls, according to authorities.
Baldwin is said to have been told the firearm was safe when he started rehearsing a scene which involved him pointing the gun at the camera.
During a press conference on Wednesday, sheriff Mendoza said there was "some complacency" on the set but it is yet to be determined if there was negligence or by whom.
About 500 rounds of ammunition have been recovered from the set, thought to include dummies, blanks and suspected live rounds.
FBI experts will make the final determination but the sheriff said he suspects more live rounds will be confirmed.
He refused to speculate on how they could have come to be found on the set. That point will prove key in the investigation.
The case is large and complex, prosecutors said, and could take months to complete.
Production on Rust has been paused while authorities investigate and producers have launched their own probe into the killing, while experts predicted a significant legal fallout.