Fox News has warned Tucker Carlson, who was ousted in April from a primetime hosting slot on the right-wing station, that his new show on Twitter violates the terms of his contract, US media reported Monday.

The cease-and-desist letter, reported by Axios and kingslot96 The New York Times, says that Carlson is bound by an exclusive contract until 2025, despite his departure from the Fox News airwaves on April 24.

Carlson's lawyer, Harmeet Dhillon, reacted to the reports on Twitter by saying that his "friend and client" would "not be silenced -- by the far left or by Fox News."

When contacted by AFP, Fox News did not immediately respond.

Carlson's ouster from Fox came just days after the Rupert Murdoch-owned company paid a whopping $787.5 million to settle a defamation lawsuit brought by the election technology firm Dominion Voting Systems.

Railing against everything from immigration policies to gun control, Carlson's show, "Tucker Carlson Tonight," pilloried liberal trends in modern America, appealing to viewers' outrage and propelling the show to the heights of cable television.

Carlson announced a few weeks after his departure that he would be setting up a show on Twitter, whose billionaire owner Elon Musk has made efforts to make the platform a welcome place for conservatives.

Since then he has posted two monologues, on June 6 and 8, in the same style as the opening segment of his Fox News show, which was the most-watched evening news program in the United States.

His executive producer has said the next installment of his Twitter show would be on Tuesday, and would be a response to former president Donald Trump's indictment on federal charges.

After Carlson's departure, Fox News saw its ratings decline in May, while remaining ahead of its rivals such as MSNBC and CNN.

The first video posted by Carlson, who has 8.3 million followers on Twitter, was viewed 115 million times, while the second video had 55.2 million views as of Monday evening.