In a video obtained by ABC News, Baldwin and his wife Hilaria Baldwin appeared on camera outside his Vermont home.
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"I'm not allowed to make any comments because it's an ongoing investigation," Baldwin told those gathered. "I've been ordered by the Sheriff's Department in Santa Fe. I can't answer any questions about the investigation. I can't."
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Hutchins died after Baldwin discharged a prop gun on the set of his film. She was 42.
The movie's director, Joel Souza, 48, was wounded in the shoulder.
"She was my friend," Baldwin told the paparazzi about Hutchins. "The day I arrived in Santa Fe to start shooting I took her to dinner with Joel the director."
Baldwin's wife attempted to interrupt him and he said, "excuse me" to wave her off as he said, "We were a very very ... well-oiled crew shooting a film together and then this horrible event happened."
Authorities are investigating the shooting.
On Wednesday, Sheriff Adan Mendoza said at a joint news conference between the Santa Fe County Sheriff's Office and district attorney's office that Baldwin fired a "suspected live round."
"The facts are clear: a weapon was handed to Mr. Baldwin," Mendoza said. "The weapon is functional and fired a live round, killing Ms. Hutchins and injuring Mr. Souza."
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Baldwin reiterated in the more the four-minute-long video posted Saturday that he has been told multiple times that he is not allowed to talk about the ongoing investigation.
He invited other questions, and Baldwin's wife got upset when one of those asking could not remember Hutchins' name.
"Her name is Halyna," Hilaria said. "If you're spending this much time waiting for us you should know her name."
Baldwin said he met with Hutchins' husband and her young son after the incident, but said he "wouldn't know how to categorize" how the meeting went.
"The guy is overwhelmed with grief," Baldwin said. "There are incidental accidents on film sets from time to time, but nothing like this. This is a one in a trillion episode."
The actor, who is also producing "Rust," said he is in "constant contact" with Hutchins' husband and son who are "in shock."
"We are eagerly awaiting the Sheriff's Department telling us what their investigation has yielded," Baldwin said.
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He said he couldn't answer whether or not he would ever work on another film set that involved firearms like those used on the set of "Rust."
"I do know that an ongoing effort to limit the use of firearms on film sets is something I'm extremely interested in," Baldwin said. "But remember, something that I think is important and that is how many bullets have been fired in films and TV shows in the last 75 years? This is America. How many bullets have gone off, nearly all of them without incident."
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In the case of something going wrong and in the wake of "this horrible catastrophic thing some new measures have to take place," he said, including the possibility of using rubber guns or plastic guns.
"That's not for me to decide," Baldwin stated. "It's urgent that you understand I'm not an expert in this field so whatever other people decide is the best way to go in terms of protecting people's safety on film sets I'm all in favor of and I will cooperate with that in any way that I can."
The Baldwins, who have six children together, declined to say why they were staying in Vermont and asked to no longer be followed as they said their children were in the car crying because they were being pursued.
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ABC Owned TV Stations contributed to this report.