Libya's interim leader today gave forces loyal to deposed ruler Muammar Gaddafi a four-day deadline to surrender towns still under their control or face military force.
As the hunt for Gaddafi himself goes on, Libyan officials accused neighbouring Algeria of an act of aggression for admitting his fleeing wife and three of his children.
Algeria's Foreign Ministry said Gaddafi's wife Safia, his daughter Aisha and his sons Hannibal and Mohammed had entered Algeria yesterday morning, along with their children.
That stirred a diplomatic row just as Libya's interim council works to consolidate its authority and capture places still loyal to Gaddafi, notably the coastal city of Sirte.
"By Saturday, if there are no peaceful indications for implementing this we will decide this manner militarily. We do not wish to do so but we cannot wait longer," Mustafa Abdel Jalil, head of Libya's interim council, told a news conference.
Anti-Gaddafi forces have converged on Sirte from east and west, but have stopped short of an all-out assault in hopes of arranging a negotiated surrender of Gaddafi's birth-place.
Gaddafi has been on the run since his foes captured his Tripoli compound on 23 August and his 42-year-old rule collapsed after a six-month uprising backed by Nato and some Arab states.
A spokesman for the National Transitional Council said it would seek to extradite Gaddafi's relatives from Algeria, which is alone among Libya's neighbours in not recognising the NTC.
Nearly 60 countries have acknowledged the NTC as Libya's legitimate authority. Russia, China, India, South Africa and Brazil are among those which have so far withheld recognition.
Algeria's acceptance of Gaddafi's wife and offspring angered Libyan leaders, who want the ousted autocrat and his entourage to face justice for years of repressive rule.
They fear Gaddafi could rally an insurgency unless he is captured, although the reported death of Gaddafi's son Khamis, a feared military commander, would be a serious blow to any chance of that.
"We have promised to provide a just trial to all those criminals and therefore we consider this an act of aggression," NTC spokesman Mahmoud Shammam said.
"We are warning anybody not to shelter Gaddafi and his sons. We are going after them ... to find them and arrest them," he said, suggesting the fugitives might seek to move on from Algeria to another country, perhaps in eastern Europe.
Algeria is to close the southern part of its border with Libya due to the "precarious situation" there, Algeria's El Watan newspaper reported, citing diplomatic sources.
Abdel Jalil, the NTC chairman, called on the Algerian government hand over any of Gaddafi's sons on its wanted list.
Algeria, which previously voted against sanctions and a no-fly zone against Gaddafi, has an authoritarian government which is deeply concerned about Arab revolts lapping near its borders.
"I would argue the Algerian regime is making a major blunder, miscalculating monstrously," Fawaz Gerges, an analyst at the London School of Economics, told the BBC.
"The Algerian regime itself is not immune from the revolutionary momentum taking place in the Arab world," he said.
A visit to a Tripoli beach compound used by Gaddafi's children and members of his elite revealed a life of opulence and privilege that many Libyans could barely dream of.
Saadi Gaddafi's chalet was strewn with designer clothes, including some unworn suits, and about 100 pairs of shoes. Aisha's house boasted 13 bedrooms and gold-plated cutlery.
Anti-Gaddafi fighters now sleep in the bedrooms of their former rulers, whose gated compound has tennis courts, football pitches and dining centres, along with magnificent sea views.
Many Libyans were overjoyed at the fall of Gaddafi, which followed that of longtime rulers in Egypt and Tunisia earlier this year, but have been chilled by evidence of mass killings in Tripoli as his forces fought losing battles with rebels.
A week after Gaddafi's overthrow, Tripoli's two million people remain without running water or electricity. Banks, pharmacies and many other shops are still closed.
Despite local clear-up efforts, the stench of rotting garbage and sewage pervades the city. Men in jeeps cried "Allahu Akbar (God is greatest)" as they toured neighbourhoods, giving out containers of water from the Tripoli local council.
A council spokesman said the pumping station for Tripoli's water supply that lies in the distant desert town of Sabha, still loyal to Gaddafi, had been damaged. The big military force needed to escort a repair team of engineers was not available.
Some residents were out shopping for food ahead of the Muslim feast that marks the end of the fasting month of Ramadan. Only small groceries and vegetable markets were open.
Libyan military officials trying to mop up Sirte and other Gaddafi strongholds said Khamis Gaddafi and former intelligence chief Abdullah al-Senussi had both been killed on Saturday.
"We have almost certain information that Khamis Gaddafi and Abdullah al-Senussi were killed on Saturday by a unit of the national liberation army during clashes in Tarhouna," military spokesman Ahmed Bani said.
A US official said he could not independently confirm Khamis's death but similar information was being received from "reliable sources". Khamis has already been reported killed twice during the uprising only to re-emerge.
International Criminal Court prosecutor Luis Moreno-Ocampo said he may seek an arrest warrant for Khamis. The Hague-based ICC has already issued warrants for Gaddafi, his son Saif al-Islam and Senussi for alleged crimes against humanity.
Human Rights Watch said members of the Khamis Brigade, which
Khamis Gaddafi commanded, appeared to have killed dozens of prisoners whose burnt bodies were found in a Tripoli warehouse.
The US-based Physicians for Human Rights said in a report it had found evidence of crimes including "murder, torture, rape, forced internment and disappearance" by Gaddafi forces during their siege of Misrata earlier in the conflict.