Libya rebels celebrate inside Gaddafi compound in Tripoli (VIDEO) (UPDATES)

Heavy fighting continued in Tripoli for a third day Tuesday, with reports that rebels have breached Muammar al-Gaddafi's compound — one of the few areas still under the Libyan leader's control.

Rebel fighters managed to overrun the gates of Gaddafi's compound in the Bab al-Aziziya neighborhood of Tripoli.

Al Jazeera is reporting that rebels have entered Gaddafi's home within the compound, and were seen celebrating. Rebels are conducting a room-by-room search, CNN says.

Hundreds of jubiliant supporters followed, pouring into the compound and surrounding streets of Bab al-Aziziya. There were reports of looting of an armoury at the compound.

Earlier Tuesday, gunfire and explosions were heard near a hotel held by troops loyal to Gaddafi, as well as the area around his compound in Bab al-Aziziya.

Rebels forces were concentrating their firepower on Gaddafi's residence, though his whereabouts remain unknown and there is speculation he may have fled to Algeria, South Africa or Angola.

Unconfirmed reports from Reuters say that Nato was also bombarding the Gaddafi compound.

An Al Jazeera correspondent said he could see smoke rising from Gaddafi's compound.

The battle is certainly not over. The city is on a knife edge.

A Nato spokesman said the alliance would continue its operations in Libya, while there were reports Tuesday of Nato planes flying low over Gaddafi's compound.

(Read more on Global Post: Seif al-Islam, Gaddafi's son, resurfaces and taunts rebels and Oil price spikes on fears for prolonged Libyan crisis)

Meanwhile the al-Mansoura district was also subject to fierce clashes on Tuesday between rebels and pro-Gaddafi forces.

Both sides claim they control most of the capital.