Israel asked Maj Gen Aroldo Lazaro to convey the message to Prime Minister Najib Mikati and Parliament Speaker Nabih Berri at a meeting in Beirut on Monday.
Under 2006 UN resolution 1701, which followed a fierce 34-day conflict between Israel and Hezbollah that killed more than 1,000 Lebanese civilians and 44 Israeli civilians, the UN peacekeeping force was reinforced near the Blue Line, which marked Israel's withdrawal from Lebanon following its occupation of the south of the country, between 1985 and 2000.
Lebanon’s army was still allowed to patrol in the area, while Hezbollah was asked to pull its fighters back from a zone patrolled by the UN peacekeepers.
About 200 Hezbollah fighters and 121 Israeli soldiers died in the 2006 war. Fears that fighting would break out again have grown in recent months because Israel accuses Hezbollah of illegally building outposts along the border.
The UN peacekeeping force, Unifil, has acknowledged it has difficulty in getting to some areas where Hezbollah has allegedly built structures.
Lebanon Foreign Minister Abdallah Bouhabib said Lebanese leaders told the UN commander that Israel should withdraw its troops from the Lebanese part of the town of Ghajar that was captured by Israeli troops in 2006.
Israel filed a complaint with the UN in June claiming that Hezbollah had set up tents several dozen metres inside of Israeli territory. It is unclear what was inside the tents or what they were for.
The area where the tents were erected in Shebaa Farms and the Kfar Chouba hills were captured by Israel from Syria during the 1967 war and are part of Syria’s Golan Heights that Israel annexed in 1981.
The Lebanese government said the area belongs to Lebanon.
Israeli media reported this month that Hezbollah evacuated one of the two tents but there has been no confirmation from the Iran-backed Lebanese group.
After the meeting between Mr Mikati and Gen Lazaro, Mr Bouhabib told reporters that the UN team has relayed the Israeli request that the tent be removed.
He added that Lebanese officials told Gen Lazaro that “we want them (Israelis) to withdraw from Ghajar that is considered Lebanese territory.”
Israel captured Ghajar from Syria in the 1967 war when it took the Golan Heights. After the Israeli military ended an 18-year occupation of southern Lebanon in 2000, UN surveyors split Ghajar between Lebanon and the Israeli-controlled Golan, but Israel reoccupied the northern half during the 34-day war with Hezbollah in 2006.
In recent weeks, Lebanese officials said that Israel has built a wall around the Lebanese part of Ghajar, warning that Israel might annex it to the Israeli part of the town.
Hezbollah last week issued a statement calling Israel’s works around the Lebanese part of Ghajar as “dangerous”, adding that the wall is separating the town “from its natural and historic surroundings in Lebanon”.
Almost at the same time that the Hezbollah statement on Ghajar was issued, an anti-tank missile was fired from Lebanon near Ghajar – with some fragments landing in Lebanon and others inside Israeli territory. Israel fired shells on the outskirts of Kfar Chouba.
Israel and Hezbollah fought to a draw in a month-long war in Lebanon in 2006.
Last month, Hezbollah said it shot down an Israel drone flying over a village in southern Lebanon.
Israel considers Hezbollah its most serious immediate threat, estimating it has some 150,000 rockets and missiles aimed at Israel.