Hassan Nasrallah said during a speech that one of the drones had been flying low among buildings and was clearly on a military "suicide mission," which he called "clear aggression."
Officials of Iran-backed Hezbollah denied firing at the drones. Spokesman Mohammed Afif said the first drone fell on the roof of a building holding the group’s media office in the Moawwad neighborhood in Dahyeh, the group's stronghold in southern Beirut.
Afif said the second drone appeared to have been sent in search of the first when it exploded in the air and crashed in an empty plot behind the building, blowing out windows in nearby structures.
There was no immediate Israeli comment on the drone incident or Hezbollah's remarks.
Nasrallah further promised retaliation at an unspecified time against Israel after he said two of its members were killed Saturday by an Israeli airstrike in Syria.
Israel said the airstrikes were to thwart an imminent drone strike against Israel by Iran's Revolutionary Guards' Al Quds Force.
Nasrallah said the strikes actually hit a Hezbollah rest house, marking a rare acknowledgment of member deaths in Syria by Israeli strikes.
Hezbollah and Israel fought a month-long war in 2006. The volatile border between the two countries, which remain technically in a state of war, has been mostly calm since.
The Associated Press contributed to this story.
The Associated Press contributed to this report.