UNITED NATIONS — France wants more power to block its citizens from leaving the country, while Britain is weighing whether to stop more of its citizens from coming home. Tunisia is debating measures to make it a criminal offense to help jihadist fighters travel to Syria and Iraq, while Russia has outlawed enlisting in armed groups that are “contradictory to Russian policy.”

The rapid surge of the Islamic State in Iraq and Syria, and its ability to draw fighters from across the globe, have set off alarm bells in capitals worldwide. Countries that rarely see eye to eye are now trying to blunt its recruitment drive, passing a raft of new rules that they hope will stop their citizens from joining extremist groups abroad.

The United States has seized on the issue, pushing for a legally binding United Nations Security Council resolution that would compel all countries in the world to take steps to “prevent and suppress” the flow of their citizens into the arms of groups considered to be terrorist organizations.

Recruits from 74 countries are among the estimated 12,000 foreign militants in Syria and Iraq, many of them fighting with ISIS, according to Peter Neumann, a professor at King’s College London, who has culled the figures largely from government sources. The largest blocs of these fighters come from nearby Muslim countries, like Tunisia and Saudi Arabia, but smaller contingents come from countries as far away and disparate as Belgium, China, Russia and the United States.