On Saturday night, "one of the Israel enemy's reconnaissance drones violated Lebanese air space... overflew the southern suburbs and left," the army said in a statement.
On August 25, two explosives-laden drones were sent to the same area. One of them exploded, sparking a dangerous escalation between Hezbollah and Israel.
The Iran-backed Hezbollah is represented in Lebanon's government and parliament but is considered a terrorist organisation by Israel and Washington, which has stepped up the financial pressure on the organisation.
The August incident heightened regional tensions, which culminated in a cross-border exchange of fire in early September.
Lebanon's government and Hezbollah chief Hassan Nasrallah both described the apparently botched operation as an act of aggression.
Israel's and Hezbollah's respective patrons, the US and Iran, have been locked in an escalating tit-for-tat proxy war in recent months.
Lebanon's defence minister, Elias Bou Saab said that the data retrieved from the intact drone - from which the explosive charge was purportedly removed for the press conference - offered a set of detailed times and locations.
The operation was initiated 11.6 kilometres (7.2 miles) off the coastal airstrip of Habonim, south of the Israeli city of Haifa, he said, adding that the explosives-laden device had been guided by another larger drone in the area.
To reach its presumed target, that device flew over the Jnah district near Beirut International Airport, in what the defence minister said would have posed a risk to civilian air traffic.
Following the Beirut incident, Hezbollah had vowed to take down Israeli drones overflying Lebanon and on 9 September claimed it had downed and seized one.
The Israeli army confirmed that one of its devices "fell" in Lebanon but it has not commented on the 25 August incident.
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