“When the Resistance carries out [an operation] it claims it immediately,” Fayyad told Sawt al-Shaab radio on Monday.
The Hezbollah official said that launching this rocket had a “political function” that aims to cause tension in the region.
Lebanese security sources said rocket was fired from south Lebanon towards Israel on Sunday , and residents of a northern Israeli town reported hearing a blast.
The incident came amid heightened tensions in the region over Syria’s civil war. Damascus has said it will respond to Israeli air strikes earlier this month against suspected Iranian missiles in Syria destined for the Lebanese militant group Hezbollah.
The rocket launch could be heard from the Lebanese town of Marjayoun, about 10 km (six miles) from the Israeli border, residents in the Lebanese town said.
Earlier on Sunday, two rockets were fired into a Shiite district of southern Beirut after Hezbollah leader Hassan Nasrallah pledged his Shi’ite Muslim guerrilla group would fight in Syria until victory for President Bashar al-Assad.
Assad is battling a two-year rebellion in which the United Nations says at least 80,000 people have been killed.