Gov. Gavin Newsom of California sued Fox News on Friday, accusing the network of defaming him in its coverage of a phone call he had with President Trump this month.

The suit, filed in Delaware, where Fox News is incorporated, seeks damages of at least $787 million and a court order prohibiting Fox from broadcasting or posting segments that mistakenly say Mr. Newsom lied about his call with Mr. Trump.

Mr. Newsom has adopted an increasingly combative approach with the president since Mr. Trump sent military troops to Los Angeles this month amid his administration’s immigration crackdown. The governor, a Democrat, is taking a page from the president by suing a news media outlet over coverage.

Mr. Newsom’s lawyers also sent Fox News a letter demanding a formal retraction and an on-air apology from Jesse Watters, a host who said on his show that Mr. Newsom had lied about the call with the president. If those conditions are met, the letter states, Mr. Newsom will dismiss the lawsuit.

The punitive damages sought by Mr. Newsom mirror the amount that Fox News agreed to pay in 2023 to settle a lawsuit by Dominion Voting Systems that accused the network of publicizing false election conspiracies that damaged the company.

“If Fox News wants to lie to the American people on Donald Trump’s behalf, it should face consequences — just like it did in the Dominion case,” Mr. Newsom said in a statement. “I believe the American people should be able to trust the information they receive from a major news outlet.”