It is the prime suspect in last week's bombing of a busload of Israeli tourists in Bulgaria and has been linked to a series of failed terror plots throughout Europe and Asia.

Four of its operatives stand charged by a United Nations tribunal in the bombing assassination of Lebanon's prime minister. And it is responsible for the most American casualties in a terror attack other than 9/11.

But European Union ministers cannot bring themselves to designate Hizballah as a terrorist group. On Tuesday, the group rejected a direct request by Israeli Foreign Minister Avigdor Lieberman to blacklist the Lebanese-based Iranian terror proxy. The move would isolate Hizballah and make it illegal to engage in transactions with the group and its members.

"Should there be tangible evidence of Hezbollah engaging in acts of terrorism, the EU would consider listing the organization," said EU President Erato Kozakou- Marcoullis, who also is the foreign minister of Cyprus.

The United States designated Hizballah in 1997 and again in 2001. But the EU requires unanimous support from its 27 member nations for such action, the Jerusalem Post reports. And that hasn't happened, although many EU countries individually have made the designation.

Hizballah "is an organization that comprises a political party [and a] social services network, as well as an armed wing," Kozakou-Marcoullis said. It has a prominent role in Lebanon's government and "plays a specific role with regard to the status quo in Lebanon."

If the U.N. Tribunal is right, it helped shape that status quo by blowing up Lebanon's popular former Prime Minister Rafik Hariri in 2005. Four Hizballah operatives are scheduled to be tried in absentia next year. Investigators traced mobile phone records to show identify the defendants' and trace their steps.

Israel, meanwhile, claims to have "unquestionable, fully substantiated intelligence" that the Bulgaria attack, which killed five Israelis and a Bulgarian bus driver, was carried out by Hizballah with Iran's support.

The Post report cites a source who says France is the biggest obstacle to a full EU designation, citing concerns it might lose influence in Lebanon if it went along with the request.