"A Lebanese army position in the district of Al-Adeesa in south Lebanon saw a drone and they fired at it, and it returned to the occupied lands," a military source told AFP, referring to Israel.

"The fire comes in the context of previous instructions that any Israeli movement inside Lebanese territory should immediately be fired at," the source said.

The National News Agency said the army opened fire at the drone after "its violation of Lebanese airspace".

Lebanon on Tuesday stressed its right to defend the country "by any means" after an alleged Israeli drone attack hit the Beirut stronghold of the Hezbollah movement.

According to Iran-backed Hezbollah, the pre-dawn attack on Sunday in the south of the Lebanese capital involved two drones -- one which exploded and another that crashed without a blast due to a technical failure.

The explosion caused damage to a media centre run by the Shiite movement, a spokesman said.

Israel has not claimed responsibility for the incident.

Israeli Prime Minister Benjamin Netanyahu on Tuesday warned Lebanon, Hezbollah's chief Hassan Nasrallah and the head of Iran's elite Quds Force to "be careful".

He suggested that Nasrallah "calm down" after the latter in a televised speech late Sunday warned of retaliation for the Beirut drone incident.

Sunday's alleged attack came a day after Israel launched strikes in neighbouring Syria to prevent what it said was an impending Iranian drone attack on the Jewish state.

Nasrallah on Sunday said two Hezbollah fighters were among those killed in the strikes.

Israel and Hezbollah have fought several wars, the last in 2006.

Hezbollah, considered a terrorist organisation by Israel and the United States, is a major political actor in Lebanon and a key government backer in war-torn Syria.