SpaceX has fired employees who helped write and distribute an open letter criticizing Chief Executive Officer Elon Musk's behaviour, the New York Times reported on Friday, citing three employees with knowledge of the situation.

SpaceX President Gwynne Shotwell sent an email saying the company had investigated and "terminated a number of employees involved" with the letter, the New York Times said.

It was unclear how many employees were terminated, the report said.

SpaceX did not immediately respond to a Reuters request for comment.

A group of SpaceX employees derided Musk as a "distraction and embarrassment" in an internal letter to executives.

In a list of three demands, the letter says "SpaceX must swiftly and explicitly separate itself from Elon's personal brand."

It added: "Hold all leadership equally accountable to making SpaceX a great place to work for everyone" and "define and uniformly respond to all forms of unacceptable behavior."

(Reporting by Baranjot Kaur in Bengaluru; Editing by Shailesh Kuber)