Just before millions of people gathered to march in France last Sunday in defiance of the attacks, the interior ministers of 11 European countries huddled quietly in Paris to draw up measures to combat potential threats — in particular, officials said, more vigilance against radical material on the Internet and social media; more intense swapping of data among governments, especially no-fly lists; and a crackdown on illegal sales of weapons.

“The threat has increased,” said Rob de Wijk, director of The Hague Center for Strategic Studies in the Netherlands, pointing to the sharp increase in arrests for religion-inspired terrorism, which Europol statistics show rose to 216 arrests in 2013 from 110 in 2009. Even as governments are ramping up their counterterrorism efforts, though, they are igniting a growing debate about whether they are going too far, too fast, and are at risk of sacrificing civil liberties as they scramble to intensify security. The trade-offs are not always easy to discern at a time when there is clear evidence of a threat from a small but potentially dangerous group of residents of their own countries.

American intelligence agencies have estimated that 18,000 foreigners, including 3,000 Europeans and other Westerners, have traveled to Syria and Iraq since the fight in the region broke out in 2011. Of those, more than 500 veterans of the fighting are estimated to have returned to Europe, according to research by Richard Barrett, a former British intelligence officer.

The three gunmen in the Paris attacks, Saïd and Chérif Kouachi and Amedy Coulibaly, had all been monitored at various points by French law enforcement and intelligence agencies but were nonetheless able to plan and execute attacks on the satirical newspaper Charlie Hebdo and a kosher supermarket.

The handling of their cases has prompted widespread debate about whether Europe has adequate resources to track not just citizens traveling to and from Syria but a broader group of radicalized Muslims who could be potential threats to act alone or in loose affiliation with militant groups like the Islamic State and offshoots of Al Qaeda. Security agencies are clamoring for more money and powers to keep up.