Israeli warplanes shot down the unmanned plane, but the infiltration marked a rare breach of Israel's tightly guarded airspace. Hezbollah had been the leading suspect because of its arsenal of sophisticated Iranian weapons and a history of trying to deploy similar aircraft.
With a formidable arsenal that rivals that of the Lebanese army, Hezbollah is already under pressure in Lebanon from rivals who accuse it of putting Lebanon at risk of getting sucked into regional turmoil. Confirmation that Hezbollah was behind the drone could put the group under further strain internally as it pursues its longstanding conflict with Israel.
Hezbollah, a powerful Shiite group committed to Israel's destruction, has long served as an Iranian proxy along Israel's northern border. It is also seen as a close ally of the embattled regime of Syrian President Bashar Assad. Israel accuses the Assad government of allowing Iran to ferry weapons to Hezbollah through its territory.
Israel and Hezbollah fought a brutal monthlong war in mid-2006. Hundreds of people were killed, and Hezbollah fired several thousand rockets and missiles into Israel before the conflict ended in a stalemate.
Israel routinely sends F-16 fighter planes over Lebanon, in violation of a U.N. Security Council resolution that ended the 2006 war. The Israeli planes have often broken the sound barrier over Beirut and other places as a show of strength, most recently after the drone incident.
"This statement today is a claim of responsibility by the Islamic resistance for this qualitative operation" of dispatching the drone, Nasrallah said in a televised address late Thursday.
"Today we are uncovering a small part of our capabilities, and we shall keep many more hidden," he said. "It is our natural right to send other reconnaissance flights inside occupied Palestine ... This is not the first time and will not be the last. We can reach any place we want" in Israel, he said.
He said the aircraft was launched from Lebanese territory and flew "tens of kilometers" over sensitive Israeli installations before it was discovered and shot down by the Israeli air force near the Dimona nuclear reactor in Israel's southern desert.
He dismissed an Israeli military statement that it began tracking the aircraft over the Mediterranean but waited until it was over an empty desert area to bring it down in order to avert casualties on the ground.
Nasrallah claimed the group had more surprises and would not hesitate to use them in any future war with Israel.
Launching the drone was a rare and provocative move by the Lebanese militants at a time of soaring regional tensions, with both Syria and Iran under intense international pressure.
Nasrallah said the aircraft was made in Iran and assembled by Hezbollah, adding that it was much more sophisticated than drones it sent before.
Hezbollah has attempted to send unmanned aircraft over Israel on several occasions, dating back to 2004. Nasrallah has claimed that the group's drones were capable of carrying explosives and striking deep into Israel.
Israel has said the latest drone was not carrying explosives and appeared to be on a reconnaissance mission.
The last known attempt by Hezbollah to use a drone took place during the 2006 war, when Israel shot down an Iranian-made pilotless aircraft that entered its airspace.
Touring southern Israel on Thursday, Israeli Prime Minister Benjamin Netanyahu praised efforts to prevent land infiltrations from Egypt. He mentioned that Israel has been equally successful "in the air, just like we thwarted the Hezbollah attempt last weekend," his first public statement blaming Hezbollah.
Hezbollah was formed to oppose Israel's occupation of south Lebanon in the 1980s, and the two sides have a bitter history.
Hezbollah has accused Israel of assassinating a top Hezbollah operative in 2008 in Syria. The group and Lebanese officials say they have broken up several Israeli spy rings inside Lebanon over the past few years.
Israel charges that Hezbollah, with Iranian backing, was behind a string of attempted attacks on Israeli diplomatic targets in India, Thailand and the former Soviet republic of Georgia, plus a deadly bombing this year that killed five Israeli tourists in a Bulgarian resort.
Last week, Israel announced the arrest of an Arab citizen it accused of spying for Hezbollah, the latest in a string of such cases.
Nasrallah also denied reports that Hezbollah members were fighting alongside Assad's forces against rebels in Syria.
The reports gained new urgency in the past weeks after Hezbollah buried several of its members, saying they died while performing their "jihadi duty." Lebanese officials said they died in Syria.
He said those killed were among 30,000 Lebanese who live in Syrian territory along the border with Lebanon and were defending themselves against repeated attacks by gunmen in Syria.
"Until this moment we did not enter the fight alongside the (Syrian) regime," Nasrallah said, but did not preclude the possibility that the group might do so in the future.