BAGHDAD—Citizens of the seven countries identified by President Donald Trump for a 90-day visa ban who hold dual nationality also will be barred from entering the U.S., State Department officials said Saturday.

The 90-day visa moratorium extends beyond just citizens of Iraq, Iran, Somalia, Sudan, Syria, Libya and Yemen, the officials said.

It also applies to people who originally hail from those countries but are traveling on a passport issued by any other nation, the official said. That means Iraqis seeking to enter the U.S. on a British passport, for instance, will be barred, according to a U.S. official. British citizens don’t normally require a visa to enter the U.S.

“Travelers who have nationality or dual nationality of one of these countries will not be permitted for 90 days to enter the United States or be issued an immigrant or nonimmigrant visa,” a State Department official said. “Those nationals or dual nationals holding valid immigrant or nonimmigrant visas will not be permitted to enter the United States during this period. Visa interviews will generally not be scheduled for nationals of these countries during this period.”

The dual-citizenship ban doesn’t apply to U.S. citizens who are also citizens of the seven nations singled out by Mr. Trump.