PARIS — As thousands of Iraqi troops slowly encircle the city of Mosul, Defense Secretary Ashton Carter met here Tuesday with key coalition members, suggesting that the battle for the Islamic State’s de facto capital in northern Syria could soon begin.

Carter spoke alongside French Defense Minister Jean-Yves Le Drian, discussing what will come after the last Islamic State fighters are purged from Mosul and the coalition sets its sights on Raqqa, Syria. Carter said the U.S.-led coalition is helping to build the local force, including a contingent of Arab fighters, that will be used to enter Raqqa. The volunteers willing to participate could soon find themselves in a protracted and violent urban battle that could serve as the Islamic State’s last stand before it morphs into an insurgency.

A U.S. military official, speaking on the condition of anonymity, said the U.S.-led coalition hopes to grow the current contingent of U.S.-backed fighters in Syria by a “couple hundred” before the force goes into Raqqa, hopefully using past military successes as a groundwork for their recruitment.

“There will be overlap,” Carter said of the current campaign in Mosul and the future campaign in Raqqa, adding that both operations are proceeding on schedule.

Earlier in the year, U.S. military officials suggested that the campaigns to retake Mosul and Raqqa could happen simultaneously. But with Mosul three times the size of Raqqa, Iraqi forces need to make considerable gains in Mosul before the coalition can muster enough resources to support both operations, the military official said.

Officials also discussed Tuesday what form the Islamic State will take if indeed it is defeated in Syria and Iraq. Carter said the coalition must be “ready for anything” and that he has directed the U.S. Joint Special Operations Command to combat militants’ current and future attacks against the West.

While the fight for Raqqa could be months away, more than 30,000 Iraqi troops are slowly inching toward the center of Mosul in the campaign that began earlier this month to retake the Islamic State stronghold.