BERLIN — As American officials sound the alarm over what they call a resurgent threat from the Shiite militant group Hezbollah, thousands of its members and supporters operate with few restrictions in Europe, raising money that is funneled to the group’s leadership in Lebanon.

Washington and Jerusalem insist that Hezbollah is an Iranian-backed terrorist organization with bloody hands, and that it is working closely with Tehran to train, arm and finance the Syrian military’s lethal repression of the uprising there. Yet, the European Union continues to treat it foremost as a Lebanese political and social movement.

As Israel heightens fears of a pre-emptive strike on Iran’s nuclear sites, intelligence analysts warn that Iran and Hezbollah would respond with attacks of their own on targets abroad. Israeli and American officials have attributed the Bulgarian bus bombing last month that killed six people, including five Israeli tourists, to Hezbollah and Iran, saying it was part of a clandestine offensive that has included plots in Thailand, India, Cyprus and elsewhere.

While the group is believed to operate all over the Continent, Germany is a center of activity, with 950 members and supporters last year, up from 900 in 2010, Germany’s domestic intelligence agency said in its annual threat report. On Saturday, Hezbollah supporters and others will march here for the annual Jerusalem Day event, a protest against Israeli control of that city. Organizers told the Berlin police that the event would attract 1,000 marchers, and that two counterdemonstrations were also likely.