Hundreds of demonstrators ran through corridors in the building smashing offices as they vented their anger of the deaths.
Smoke was seen rising from parts of the building as UN security troops struggled to contain crowds.
The anger erupted after an Israeli bombing raid killed at least 54 people, 37 of them children, as they slept in the early hours of Sunday morning.
Lebanese media reported that dozens of people remained trapped inside the three-storey building. Some of them had fled the Israeli bombardment of the Lebanese coastal town of Tyre.
Yasir Abu Hilala, Aljazeera's correspondent in Qana, said aid workers had pulled out only three people alive.
Efforts to get the wounded to hospital have been hampered as all roads around Qana have been destroyed by Israeli air strikes, he said.
The Israeli army has rejected responsibility for the deaths, saying that Hezbollah bore the blame because it used the village as a site for launching rockets.
However Hasan Fadlallah, a Hezbollah MP, told Aljazeera that Israel had committed "a new massacre".
"This massacre will enhance the Lebanese people's determination to endure Israeli aggression and will increase the [Hezbollah] resistance's determination to confront this enemy," he said.
"Israel is mistaken and deceived if it believes it can break the will of the Lebanese people in this way."
The attack came as Hezbollah fighters battled Israeli forces making a new thrust into southern Lebanon, Lebanese security sources said on Sunday.
Fighting erupted when Israeli forces crossed the border from the Israeli village of Metula towards the town of Khiam after aircraft and artillery strikes.
The Israeli army said a new wave of Hezbollah rockets hit the Israeli towns of Nahariya, Kiryat Shemona and an area close to Maalot, although no injuries were reported.
An Israeli missile strike hit the main Lebanese border crossing into Syria on Sunday, forcing it to close for the first time since the conflict began more than two weeks ago.
Israeli fighter jets fired three missiles at the Masnaa crossing, which is about 300m beyond a Lebanese customs post. No casualties were reported in the strike.
The passage has been an escape route for tens of thousands of Lebanese fleeing the fighting into Syria after Israel bombed Beirut airport.
The bodies of eight civilians were found near Tyre after Israeli missile strikes on Saturday, Salam Daher, the Lebanese civil defence chief, said.
Rescue workers say dozens more civilians, including a large number of children, are still buried in the rubble of houses destroyed in attacks around the city.
The Lebanese health minister has said the recovery of bodies in the south could raise the toll from the fighting.
Up to 600 Lebanese people, mainly civilians, are thought to have died in the offensive. Fifty-one Israelis have also been killed since Israel launched its offensive in mid-July after the kidnapping of two of its soldiers and rocket attacks by Hezbollah fighters.