The Israeli raids in the early hours of Thursday had prompted concern that Iran's powerful ally Hezbollah could retaliate from its positions in southern Lebanon.
"We are monitoring the overall situation, but in relation to our area, the situation has been quiet," said Andrea Tenenti, spokesman for the UN Interim Force in Lebanon (UNIFIL).
Tenenti told AFP that the UN force had not increased its patrols in the south, which number around 450 per day.
On Thursday morning, Israel carried out unprecedented strikes against what it said were Iranian logistics and intelligence targets in Syria.
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It said the strikes were in response to rocket fire towards its forces in the occupied Golan Heights, which it blamed on Iran's Quds Force.
Iranian forces are deployed in Syria to back the regime of President Bashar al-Assad, whose fighters have also received a boost from Iraqi and other foreign militias as well as Hezbollah.
Israel, which has vowed to prevent any entrenched Iranian military presence in southern Syria, is suspected of carrying out several rounds of strikes against Tehran-backed forces.
It has also targeted what it says are arms deliveries to Hezbollah in Syria.
There was no immediate comment from Hezbollah on the latest Israeli strikes or how it might respond.
Israel and its US ally believe the Lebanese Shiite militia is amassing weapons on Lebanon's southern border in preparation for a new war, after a deadly conflict with Israel in 2006.
Set up in 1978, UNIFIL was beefed up after the 2006 war and tasked with guaranteeing a ceasefire and Israeli withdrawal from a demilitarised zone on the border.
UNIFIL now has 10,500 troops on the ground, monitoring the truce and helping Lebanese troops secure the borders.