The warrant was issued by a Santa Fe court in New Mexico - the state where the movie Rust was being filmed.

The document relates to an Apple iPhone that is "believed to be in his possession".

The court is seeking access to iMessages exchanged between Baldwin and an unnamed person.

It comes almost a week after the actor was seen in public for the first time since the fatal shooting of Halyna Hutchins at the end of October.

The director of photography died after a prop gun held by Baldwin, 63, went off accidentally - shooting and killing her while filming the western.

The film's director, Joel Souza was also injured.

Last week, in his first TV interview since the accident, Baldwin told ABC television's George Stephanopoulos that he did not pull the trigger.

Baldwin sobbed as he said: "Well the trigger wasn't pulled, I did not pull the trigger...

"No, no, no, no, no, I would never point a gun at anyone and pull a trigger at them, never."

Asked "how did a real bullet get on that set?", the actor replied: "I have no idea, someone put a live bullet in a gun, a bullet that wasn't even supposed to be on the property."

Read more:
Who was Halyna Hutchins? Tributes to 'brilliant' cinematographer killed on film set
What other fatal accidents have happened on movie sets?