Fox News has demanded that Tucker Carlson stop posting videos to Twitter, escalating the dispute between the network and its former star host over how — and if — he can continue to speak publicly since his prime-time show was canceled in late April.

In a letter sent to Mr. Carlson from Fox lawyers, the network accused him of violating the terms of his contract, which runs until early 2025 and limits his ability to appear in media other than Fox. The letter is labeled “not for publication,” in all caps.

Since Mr. Carlson was ousted by Fox News, he has begun producing a bare-bones version of his Fox program, “Tucker Carlson Tonight,” and posting it directly to Twitter. The new show, called “Tucker on Twitter,” bears some of the hallmarks of his prime-time show on Fox, including a monologue focused on current affairs and cultural issues.

Harmeet K. Dhillon, a lawyer representing Mr. Carlson, said in a statement that Fox News’s legal threat was not in the interest of the network’s audience.

“Doubling down on the most catastrophic programming decision in the history of the cable news industry, Fox is now demanding that Tucker Carlson be silent until after the 2024 election,” the statement read. “Tucker will not be silenced by anyone.”

Axios earlier reported that Fox sent Mr. Carlson the cease-and-desist letter.

A spokeswoman for Fox News said the network had no comment.