NATO unleashed its heaviest bombing of the Libyan capital since air strikes began in March, but Muammar Gaddafi vowed to fight to the end.
Sustained attacks continued through Tuesday and into the night after warplanes hit the city several times an hour, hour after hour, in an onslaught the Libyan leader's government said killed 31 people.
Describing planes overhead and explosions around him, Gaddafi spoke defiantly after strikes on his Bab al-Aziziya compound.
"We only have one choice: we will stay in our land dead or alive," Gaddafi said in a fiery audio address on state television.
It later showed images of what it said was a meeting between Gaddafi and tribal leaders on Tuesday.
U.S. President Barack Obama said in Washington there was significant progress in the operation and it was "just a matter of time before Gaddafi goes."
At least 31 people were killed in 60 strikes on the Libyan capital in the raids, government spokesman Moussa Ibrahim told reporters. His account could not be independently verified.
"How could the world sleep tonight knowing that armies of such evil are willingly and knowingly attacking a peaceful capital with 60 rockets and killing people ... while there is a way out of this. To sit down, talk and negotiate," Ibrahim said.
A British defense official said several operations carried out by fighter aircraft had targeted Gaddafi's secret police headquarters and a military installation on Tripoli's southwestern outskirts.
Gaddafi's troops and the rebels have been deadlocked for weeks, neither able to hold territory on a road between Ajdabiyah in the east, which Gaddafi's forces shelled on Monday, and the Gaddafi-held oil town of Brega further west.
Rebels control the east of Libya, the western city of Misrata and the range of mountains near the border with Tunisia. They have been unable to advance on the capital against Gaddafi's better-equipped forces.
Gaddafi forces pulled back to high ground in the Western Mountains outside Yafran, 130 km (80 miles) southwest of Tripoli. The rebels broke a long government siege of the town on Monday.
But a rebel commander in Zintan, in the same region, said Gaddafi's forces were massing on Tuesday in their biggest numbers in the area since the start of the conflict.
Diplomatic overtures were being made to the rebels by world powers, including Russia and China, despite their misgivings about interference in Libya's affairs.
A Russian special envoy for Africa said in the rebel capital of Benghazi on Tuesday that Gaddafi could no longer represent Libya and that Russia was ready to help in any way possible.
In Beijing, the Chinese Foreign Ministry said an Egypt-based Chinese diplomat had visited Benghazi for talks with the rebel-led National Transitional Council.
The Libya contact group of Western and Arab countries agreed in May to provide millions of dollars in non-military aid to help the rebels keep services and the economy running.
They meet on Thursday in the United Arab Emirates to discuss rebel plans and financing for them.