Hassan Nasrallah vows to do everything to prevent such attacks. PHOTO: REUTERS
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.
The group and Israel, which have fought several wars, have upped their belligerent rhetoric in recent months.
The pre-dawn incident in Beirut came just hours after Israel said it had launched strikes in neighbouring Syria to prevent an Iranian attack on the Jewish state.
Israeli drones in Beirut threaten Lebanon's sovereignty: PM Hariri
Nasrallah said the strike had killed two Hezbollah members.
In a televised speech broadcast to thousands of supporters, Hezbollah chief Hassan Nasrallah said the attack on a target in Beirut's south was the first such "hostile action" since the 2006 war between Hezbollah and Israel.
He said it violated a UN Security Council resolution ending the 33-day war, which killed 1,200 people in Lebanon, mostly civilians, and 160 in Israel.
Nasrallah said Hezbollah would do "everything" to prevent similar attacks.
"The time when Israeli aircraft come and bombard parts of Lebanon is over," he said.
"I say to the Israeli army along the border, from tonight be ready and wait for us," he said. "What happened yesterday will not pass."
Addressing Israelis, he said: "Do not live, do not rest, do not be reassured, and do not bet for a single moment that Hezbollah will allow... aggression of this kind."
Nasrallah said a surveillance drone had flown over the capital's suburbs, and that an armed drone had then "hit a specific area".
Earlier, the Lebanese army said two Israeli drones had violated Lebanese airspace over Beirut, and Hezbollah said one had damaged a media centre it runs in a residential building.
A Hezbollah spokesman, Mohamed Afif, said shards from shattered window panes had caused "minor injuries".
The Israeli army declined to comment on the Lebanese claims.
Earlier, Lebanon's President Michel Aoun, an ally of Hezbollah, said the drone incursion targeted "stability and peace in Lebanon and the region".
Prime Minister Saad Hariri, who is one of the group's most prominent political opponents, said the incident was "a threat to regional stability".
US Secretary of State Mike Pompeo later Sunday called Hariri to stress the "necessity to avoid any escalation", the premier's office said.
Earlier Sunday, the Israeli military said it had been able late Saturday to thwart an attempt by an Iranian force to attack northern Israel with explosive-laden drones.
Since the beginning of Syria's war in 2011, Israel has conducted hundreds of strikes in the country, most of them against what it says are Iranian and Hezbollah targets.
However, it rarely acknowledges specific operations so promptly.
Military spokesman Jonathan Conricus said the Israeli attack in Aqraba, southeast of Damascus, targeted "terror targets and military facilities belonging to the Quds force (of Iran's elite Revolutionary Guards) as well as militias".
"We've been tracking the Quds force" for weeks, he said.
"The intention was to fly a number of attack drones towards targets located in northern Israel," he said.
A Syrian military source quoted by state news agency SANA said anti-aircraft defences detected "enemy targets" late Saturday and responded.
The Syrian Observatory for Human Rights, a Britain-based monitor, said five fighters were killed, but a high-ranking official in Tehran denied Iranian positions had been hit.
Nasrallah said those strikes killed two Hezbollah members but that the site hit was a resting place, not a military facility.
"There were just Lebanese youth from Hezbollah in the place that was bombarded," he said.
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On Sunday afternoon, Prime Minister Benjamin Netanyahu toured the north of Israel.
"Any country that allows its territory to be used for aggression against Israel will face the consequences," said the veteran premier, who has sought to burnish his security credentials ahead of September elections.
Just minutes after Israel announced its raid, Netanyahu in the morning had hailed what he termed a "major operational effort" in thwarting an attack.
"Iran has no immunity anywhere," Netanyahu said. "Our forces operate in every sector against the Iranian aggression."
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