At least seven tourists, including Israeli citizens, were killed in the bombing of a tour bus in Burgas, Bulgaria, in July. The Israeli government accused Iran and Shiite movement Hezbollah of carrying out the attack.
Bulgarian Interior Minister Tsvetan Tsvetanov last week said there were signs Hezbollah was involved in the attack.
Hague told the Royal United Services Institute that the British government wanted the European Union to take "robust action" in response to the Burgas attack.
"The European Union must demonstrate that no organization can carry out terrorism on European soil without consequences," he said.
Washington and London consider Hezbollah a terrorist entity. Its political arm holds Cabinet-level positions in the Lebanese government. The ruling March 8 coalition is allied with the Shiite political movement.
"We must be clear that no state should allow terrorist groups to operate from its territory and that terrorism as a tool of foreign policy is always unacceptable," said Hague.
The European Union doesn't label Hezbollah as a terrorist entity.