Al Jazeera reported that gunfire and explosions were heard near a hotel held by troops loyal to leader Muammar al-Gaddafi, as well as the area around his compound in the Bab al-Aziziya neighborhood.
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Rebels forces seem to be concentrating their firepower on Gaddafi's residence, though his whereabouts remain unknown – with speculation he may have fled to Algeria, South Africa or Angola.
Unconfirmed reports from Reuters say that Nato is also bombarding the Gaddafi compound.
Libyan opposition radio said the rebels had succeeded in storming one of its main gates, the BBC reported.
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.
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