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.
AP writer Aron Heller in Jerusalem contributed to this report.