US President Barack Obama says Muammar Gaddafi's iron fist regime has reached a tipping point and the Libyan tyrant must leave now to avoid further bloodshed.
In a written statement, Obama also called on Libyan rebels who have surged into Tripoli to respect human rights, show leadership, preserve the institutions of the Libyan state and move towards democracy.
"Tonight, the momentum against the Gaddafi regime has reached a tipping point.
Tripoli is slipping from the grasp of a tyrant," Obama said in a statement issued while he was on holiday in Martha's Vineyard, Massachusetts.
"The Gaddafi regime is showing signs of collapsing. The people of Libya are showing that the universal pursuit of dignity and freedom is far stronger than the iron fist of a dictator."
Obama said the surest way for bloodshed to end in Libya was simple: "Muammar Gaddafi and his regime need to recognise that their rule has come to an end."
"Gaddafi needs to acknowledge the reality that he no longer controls Libya. He needs to relinquish power once and for all." Obama also noted that the United States had recognised the opposition Transitional National Council (TNC) as Libya's legitimate governing authority.
"At this pivotal and historic time, the TNC should continue to demonstrate the leadership that is necessary to steer the country through a transition by respecting the rights of the people of Libya."
He called on the rebels to avoid civilian casualties, protect the institutions of the Libyan state, and pursue a transition to democracy that is "just and inclusive for all of the people of Libya." AFP srp
An Agence France-Presse reporter said the night was mainly calm although the sound of heavy fighting was heard on Monday morning near Gaddafi's central Tripoli residence.
Fighting was also heard in the south of the capital.
By daybreak it was still not clear how much of the capital the rebels controlled. Jibril called on the insurgents to act responsibly as the battle to end four decades of dictatorship neared its end.
"The fight is not over yet," he said on rebel television Al-Ahrar. "God willing, in few hours our victory will be complete."
Thousands of residents poured onto the streets of Tripoli on Sunday night to welcome the rebels, congregating at the symbolic Green Square near the waterfront which they renamed Martyrs Square.
Sky News showed jubilant crowds, with many people waving the red, black and green flag of anti-regime forces, dancing in joy and shouting Allah Akbar (God is greatest). Some fired rifles into the air.
Similar scenes of jubilation were witnessed in Benghazi, the rebels' bastion in the east, where tens of thousands of delirious residents danced and proclaimed the end of the regime of the "tyrant" Gaddafi.
While the embattled Gaddafi spoke to the nation three times on Sunday in audio recordings, his whereabouts were unknown and he has not been seen in public for weeks.
But the 69-year-old strongman vowed not to surrender and urged the people of Tripoli to "purge the capital."
Government spokesman Moussa Ibrahim told a press conference 1300 people had been killed in the rebel assault on the capital, describing the fighting as a "real tragedy".
But there was no independent confirmation of casualties, nor any immediate indication of how much resistance may have been put up against the rebels.
Ibrahim insisted that Libya's regime "is still strong and thousands of volunteers and soldiers are ready to fight", although the reality on the ground seemed to belie his boasts.
In The Hague, the International Criminal Court confirmed that Gaddafi's son, Seif al-Islam, for whom the ICC had issued arrest warrants for crimes against humanity, was in detention.
"I have received confidential information stating he has been arrested," Luis Moreno-Ocampo said early Monday.
"We hope he can soon be in the Hague" to face justice, he said, adding that he planned to contact the "Libyan transitional government" later in the day.
Earlier, the chairman of Libya's rebel National Transitional Council (NTC), Mustafa Abdel Jalil told Al-Jazeera television from Benghazi Seif was "being kept in a secure place under close guard until he is handed over to the judiciary".
Abdel Jalil did not say when or where he had been captured. In his three audio messages broadcast on Sunday, Gaddafi remained adamant he would not relinquish power.
"We will not, we will not abandon Tripoli to the occupants and their agents. I am with you in this battle," he said in one message. "We do not surrender and, by God's grace, we will emerge victorious."
He called on his supporters to "march on Tajura in tens of thousands to purge the officials of the colonisers," in a reference to the rebels, who have since March been backed by blistering NATO air strikes on Gaddafi's military.
In another message he urged supporters to "march by the millions" to liberate cities held by "traitors and rats".