WASHINGTON—The Justice Department sued casino mogul Steve Wynn Tuesday to force him to register as a lobbyist in connection with his 2017 efforts to obtain a diplomatic favor long sought by Chinese authorities.

The lawsuit comes almost a year after the department told Mr. Wynn to register under the Foreign Agents Registration Act and signaled that it would go to court to compel him to do so if necessary, as The Wall Street Journal reported at the time, citing people familiar with the matter.