Moamer Kadhafi's wife and three children fled to Algeria, as rebels closed in on his hometown of Sirte and said the longtime strongman still posed a danger to Libya and the world.
Kadhafi and his sons Saadi and Seif al-Islam -- were reportedly holed-up in the town of Bani Walid, south of the capital Tripoli, Italian news agency ANSA said, citing "authoritative Libyan diplomatic sources".
Meanwhile a rebel minister said Kadhafi's youngest son Khamis, whose death has been announced several times since Libya's conflict erupted but never confirmed, may have been killed south of Tripoli and buried on Monday.
Algiers confirmed that Kadhafi's wife Safiya, two sons, a daughter and their children, had crossed the border into the country, prompting the rebels' National Transitional Council (NTC) to demand their return.
"The wife of Moamer Kadhafi, Safiya, his daughter Aisha, and sons Hannibal and Mohammed, accompanied by their children, entered Algeria at 8:45 am (0745 GMT) through the Algeria-Libyan border," the Algerian foreign ministry said in a statement carried by the state APS news agency, giving no information on the whereabouts of Kadhafi himself.
Scene: Anxious Libyan families await news of loved ones
The ministry said that UN chief Ban Ki-moon, the Security Council and senior Libyan rebel leader Mahmud Jibril had been informed.
So far Algeria has not recognised the NTC and has adopted a stance of strict neutrality on the Libyan conflict, leading some among the rebels to accuse it of supporting the Kadhafi regime.
Rebel spokesman Mahmud Shammam said Algeria had given them "a pass" to enter a third country, adding that the rebel leadership wanted them back in Libya.
"Saving Kadhafi's family is not an act we welcome and understand," he told a press conference. "We'd like those persons to come back."
"We can assure our neighbours that we want better relations with them ... but we are determined to arrest and try the Kadhafi family and Kadhafi himself," Shammam went on, saying the rebels guaranteed a "fair trial".
Rebel Libyan justice minister Mohammed al-Allagy told AFP that Khamis "may have been killed in battle," adding that "the rebel leader said he had been buried."
Khamis, 28, commanded a brigade seen as the most effective and loyal force of the Libyan leader.
Italy's ANSA news agency reported that Khamis had "almost certainly" been killed as he tried to make the 100 kilometre (60 mile) journey from Tripoli to Bani Walid to join his father.
Rebel chief Mustafa Abdel Jalil urged the international coalition to continue its action against the embattled strongman.
"Kadhafi's defiance of the coalition forces still poses a danger, not only for Libya but for the world. That is why we are calling for the coalition to continue its support," Abdel Jalil said at a meeting in Doha of chiefs of staff of countries taking part in military action in Libya.
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The international coalition began Operation Unified Protector on March 19 under a UN mandate which authorised air strikes to protect civilians.
Since March 31, the air strikes have been carried out under NATO command.
Coalition military chiefs said in a joint statement that the war in Libya "is yet to end" and that "there is a need to continue the joint action until the Libyan people achieve their goal by eliminating the remnants of Kadhafi."
US Secretary of State Hillary Clinton is to visit Paris on Thursday for an international Contact Group meeting on Libya in a bid to boost financial and economic support for the rebels, the State Department said.
"Libya's transition to democracy is and should be Libyan-led, with close coordination and support between the (NTC) and its international partners," said spokeswoman Victoria Nuland.
The White House said it did not know Kadhafi's whereabouts but had no indication he had left Libya.
There had been speculation that he was among tribal supporters in his hometown Sirte, 360 kilometres (225 miles) east of Tripoli, where rebel forces were gradually advancing upon.
Rebels had moved to within 30 kilometres (20 miles) of the town from the west and captured Bin Jawad 100 kilometres (60 miles) to the east, the rebel commander in Misrata, Mohammed al-Fortiya, told AFP on Sunday.
On Monday, the rebels seized the desert hamlet of Nofilia just inland from the coastal road east of Sirte, an AFP correspondent reported.
A reconnaissance force meanwhile pressed on to within 70 kilometres (45 miles) of the town, a rebel commander told AFP.
"Tomorrow, God willing, we will continue our advance. Their morale is rock bottom," the commander said.
The rebels' deputy commander in chief, General Suleyman Mahmud, said talks were still going on with civic and tribal leaders to try to broker Sirte's peaceful surrender.
The rebels have offered a $1.7 million dollar reward for Kadhafi's capture, dead or alive.
Fierce fighting also raged in the west as rebels trying to mop up resistance by loyalist forces said they were ambushed southwest of Zuwarah.
Some 70 percent of homes in central Tripoli still have no running water because of damage to the mains supply, but potable water is being distributed from mosques, giving priority to the elderly and medical facilities, NTC officials said.
China has delayed moves by Britain, France and Germany to get a UN sanctions committee to release five billion dollars of frozen Libyan assets to buy emergency aid, diplomats said.
Human Rights Watch said evidence indicated retreating Kadhafi forces had massacred dozens of detainees, after AFP counted at least 50 human skulls in a makeshift jail.
HRW said it had inspected about 45 skeletons and two other bodies at the detention centre in Tripoli's Salaheddin neighbourhood.