Heavy fighting is taking place in Tripoli around the compound of embattled Libyan leader Col Muammar Gaddafi after rebels seized control of much of the city on Sunday.
Throughout the night, jubilant crowds remained in central Green Square, previously the scene of nightly pro-Gaddafi demonstrations.
Rebels met little resistance as they swept in from east, south and west.
A rebel spokesman says pro-Gaddafi forces still control 15-20% of Tripoli.
The rebels also said they had captured Col Gaddafi's son Saif al-Islam, but there is no word of the colonel's whereabouts.
Tanks emerged from Col Gaddafi's Bab al-Azizia compound early on Monday morning and began firing, a rebel spokesman said.
Sustained gunfire has been heard in the area.
Western leaders have welcomed the rebel advance and urged Col Gaddafi to go.
The BBC's Tripoli correspondent, Rana Jawad, who has been unable to report openly since March, says people in her neighbourhood in eastern Tripoli were woken by the imam at the local mosque singing the national anthem of the pre-Gaddafi monarchy.
There is very much a sense that the end is near and the rebels have achieved what they wanted, our correspondent says.
In Green Square - which is to return to its original name of Martyrs' Square - rebel supporters tore down the green flags of the Libyan government and trampled on portraits of Colonel Gaddafi.
"Tonight, the momentum against the Gaddafi regime has reached a tipping point. Tripoli is slipping from the grasp of a tyrant," said US President Barack Obama in a statement.
UK Prime Minister David Cameron, who is cutting short his holiday to chair a meeting of the National Security Council, said it was clear "that the end is near for Gaddafi".
Mr Cameron said the Libyan leader had "committed appalling crimes against the people of Libya and he must go now to avoid any further suffering for his own people".
The International Criminal Court (ICC) has issued arrest warrants for Col Gaddafi, his son Saif al-Islam, and the head of the intelligence service, Abdullah al-Sanussi, for crimes against humanity. ICC prosecutor Luis Moreno Ocampo said he had been informed of Saif al-Islam's arrest.
Another of Col Gaddafi's sons, Muhammad, was speaking on the phone to al-Jazeera TV when he said the rebels were surrounding his home. Gunfire was heard before the line cut off.
A diplomatic source told the AFP news agency that Col Gaddafi could still be in Bab al-Azizia. He has not been seen in public since May, although he has broadcast audio messages from undisclosed locations.
TV footage showed Libyans kneeling and kissing the ground in gratitude for what some called a "blessed day".
In an audio message broadcast late on Sunday, the Libyan leader urged residents to "save Tripoli" from the rebels.
"How come you allow Tripoli, the capital, to be under occupation once again?" he asked. "The traitors are paving the way for the occupation forces to be deployed in Tripoli."
Libyan Information Minister Moussa Ibrahim told CNN that the Gaddafi government still had 65,000 loyal soldiers under its command.
However, some forces have surrendered to the rebels, including the special battalion charged with securing Tripoli.
The chairman of the rebel National Transitional Council (NTC) Mustafa Mohammed Abdul Jalil said early on Monday: "I warn you, there are still pockets of resistance in and around Tripoli."
Mr Ibrahim said fighting in the city since noon (10:00 GMT) on Sunday had left 1,300 people dead and 5,000 wounded. There is no confirmation of the figures.
Rebel forces advanced from the east and west in recent days, backed by Nato aircraft enforcing a UN resolution to protect civilians.
During the day, one group of rebels had pushed in from the west while another set up checkpoints on the eastern outskirts.
It is clear there have been bloody battles in parts of Tripoli, the BBC's Matthew Price reports from the city.
The Libyan information minister accused Nato of backing "armed gangs" with air power. He added that the Gaddafi government was prepared to negotiate directly with the NTC.
Mr Jalil said the rebels would halt their offensive if Col Gaddafi announced his departure.
Speaking about Saif al-Islam Gaddafi's capture, Mr Jalil said he was "being kept in a secure place under close guard until he is handed over to the judiciary".
He added that rebel forces would give Col Gaddafi and his sons safe passage out of the country.
