The frontier between the two countries has remained calm since Israel and Lebanon's Hezbollah traded fire on Sunday.
Israel's military said it had responded with fire into south Lebanon after anti-tank missiles targeted an army base and vehicles. Hezbollah said its fighters destroyed an Israeli armoured vehicle, killing and wounding those inside, though Israel said there were no casualties.
Hezbollah leader Sayyed Hassan Nasrallah said this week that the episode had ended but had launched a "new phase" in which his Shi'ite Muslim movement would target Israeli drones that breach Lebanon's airspace.
The long-time enemies, who last fought a month-long war in 2006, had been on alert after two drones crashed in a Beirut suburb that Hezbollah largely dominates. Nasrallah deemed the Aug. 25 incident an Israeli attack.
Aoun, a political ally of Hezbollah, has likened the crash of the drones, including one that exploded, to a "declaration of war"."Any attack on Lebanon's sovereignty ... will be met with legitimate self-defence which Israel will bear all the consequences of," Aoun's office cited him as saying on Friday in a meeting with U.N. Special Coordinator for Lebanon Jan Kubis.