UNITED NATIONS—The Security Council unanimously passed a counterterrorism resolution on Friday that authorizes the use of military force against the extremist groups Islamic State and al-Nusra Front.

The resolution, introduced by France in the wake of terrorist attacks in Paris a week ago, calls on the international community to mobilize and to organize efforts against the global threat posed by terrorism, to block the flow of foreign fighters and to crack down on terrorist finances.

A...