PARIS—U.S., French and other allies agreed they must step up the fight against Islamic State in coming months to vanquish the extremist group from its strongholds in Syria and Iraq.

U.S. Defense Secretary Ash Carter and French Defense Minister Jean-Yves Le Drian hosted a meeting of five other coalition partners on Wednesday to discuss what each could do to intensify the fight against Islamic State in Iraq, Syria and beyond. The two men said the coalition is setting its sights in the coming weeks on pushing Islamic State out...