ROME — Silicon Valley’s battle over encryption is heading to Europe.

In the United States, the F.B.I.’s demands that Apple help “unlock” an iPhone used by a mass killer in California opened a heated debate on privacy. After recent attacks on the Continent, like the bombings in Brussels last week and the wave of violence in Paris last November, governments across the European Union are increasingly pushing for greater access to people’s digital lives.

This week, French lawmakers are expected to debate proposals to toughen laws, giving intelligence services greater power to get access to personal data.

The battle has pitted Europe’s fears about the potential for further attacks against concerns from Apple and other American technology giants like Google and Facebook that weakening encryption technologies may create so-called back doors to people’s digital information that could be misused by European law enforcement officials, or even intelligence agencies of unfriendly countries.

The recent attacks have pushed many Europeans to favor greater powers for law enforcement over privacy. But opponents say such measures should not undermine the region’s tough data protection rules that enshrine privacy on par with other rights like freedom of expression.