But while the United States has stepped up efforts to interdict Hezbollah's international financial operations, the group has enjoyed greater freedom in Europe.
Germany's annual threat report in 2012 concluded that nearly 1,000 Hezbollah members and supporters lived there. Hezbollah raises money quietly in several European cities, according to intelligence agencies, to support its extensive network of social programs in Lebanon.
Only the Netherlands among the main European governments describes Hezbollah as a terrorist organization. Britain distinguishes between its military wing -- which is proscribed -- and its work as a political party in Lebanon. France and other EU states do not characterize any part of Hezbollah as a terrorist organization.
If the European Union moves toward unified sanctions against Hezbollah, the current Lebanese coalition government led by Prime Minister Najib Mikati may be in jeopardy
Mohanad Hage Ali, a Lebanese expert on Hezbollah based at the London School of Economics, told CNN, "Since Mikati formed his government two years ago, there has been steady European support. But since Hezbollah is part of this government, more EU member states are likely to dissociate themselves from Mikati's government" if the link with the Bulgaria bombing is confirmed.
"Since the 1980s," he added, "the United States listing of Hezbollah on its list of terrorist organizations has been seen as a unilateral act, while the Lebanese party was improving its international relations, especially with EU states. This may now change."
Mikati said Tuesday his government is "ready to cooperate in clarifying the circumstances" of the attack "in fairness and safeguarding justice," but he did not address the accusations against Hezbollah .
Hage Ali said that if Hezbollah were designated a terrorist group by the EU it would virtually eliminate the European role in mediating between Hezbollah and Israel on such issues as negotiating prisoner exchanges.
Germany has been especially active in mediating on humanitarian issues. But there have been signals in the past few months from senior figures in Angela Merkel's coalition that the mood is shifting.
Last August, the foreign policy spokesman for Merkel's Christian Democratic Union, Philipp Missfelder, told the Jerusalem Post it was "long overdue to place Hezbollah on the EU's list of terror organizations."
The British foreign secretary, William Hague, has also called on the EU to reopen discussions on Hezbollah's status.