To promote his administration’s decision to reimpose sanctions on Iran, President Trump turned Friday to the wildly popular television show “Game of Thrones.”

In a tweet that featured a cinematic poster with a steely depiction of the president, he included the words “Sanctions Are Coming.” That phrase mimicked one from the show, “Winter Is Coming,” a foreboding line that warns of a deep freeze that will herald an army of the undead from the north to conquer other lands.

HBO responded to Mr. Trump with a message of its own: Keep us out of it.

“We were not aware of this messaging and would prefer our trademark not be misappropriated for political purposes,” an HBO spokesman, Quentin Schaffer, said in a statement.