MEXICO CITY—Nicaraguan prosecutors charged Saturday the owner and director of the country’s leading cable news channel with inciting hatred and conspiring to commit acts of terrorism, ratcheting up pressure on the country’s beleaguered independent media.

The charges against Miguel Mora, who was detained in the capital of Managua on Friday, stem from his station’s coverage of monthslong protests against President Daniel Ortega, during which more than 300 demonstrators have been killed and thousands injured by the government’s...