ON TUESDAY the Bulgarian government confirmed what most of the world has known for months: The bombing of a bus carrying Israeli tourists in the Black Sea resort of Burgas last July 18 was carried out by members of Lebanon’s Hezbollah organization. The results of an official investigation present leaders of the European Union with a reality that will be difficult to ignore. They must decide whether to allow a terrorist attack on E.U. territory to go unpunished or to sanction a movement that is both an Iranian proxy and the dominant party in the Lebanese government.

The case for sanctions is a strong one. The Burgas attack, which killed five Israelis and wounded more than 100, was not an isolated incident but part of a campaign of terrorism against Israeli, U.S. and gulf state targets by Hezbollah and the Quds Force of Iran’s Revolutionary Guard Corps. According to a new report by Matthew Levitt of the Washington Institute for Near East Policy, the two groups decided in January 2010 to launch a campaign of violence aimed at punishing Israel for the assassination of Iranian scientists and deterring an attack on Iran’s nuclear program.

Since then the Quds Force has, among other things, plotted to kill the Saudi ambassador to the United States in Washington and the U.S. ambassador to Azerbaijan, and it has attacked an Israeli diplomat’s wife in India. Hezbollah has attempted attacks on Israeli tourists in Cyprus, Greece and Thailand as well as in Bulgaria. Mr. Levitt says that more than 20 terror attacks by Hezbollah or the Iranian force were detected between May 2011 and July 2012; fortunately, almost all failed or were disrupted.

Israel participates in this shadow war, too: Five Iranian nuclear scientists have been assassinated in recent years. The United States has sponsored cyberattacks on Iranian nuclear facilities. But nothing justifies Hezbollah’s attempts to murder tourists; one of those killed in Bulgaria was a pregnant woman. Nor should a democratic community such as the European Union tolerate terrorist attacks on its territory by an established organization such as Hezbollah, which seeks recognition as a legitimate political movement worthy of governing Lebanon.

The United States, which long ago designated Hezbollah as a terrorist organization, has been pressing European leaders to do the same so that the group’s funds in European banks and other financial assets can be targeted. Several governments, led by France, have resisted; they worry that sanctions could further destabilize Lebanon or subject European peacekeepers in the south of that country to reprisals. Bulgaria’s findings should end the debate. Inaction would mean accepting that Europe can be a free-fire zone for Iran and its proxies.