Libya's interim rebel leaders have given pro-Gaddafi forces until Saturday to surrender or face military force.
Mustafa Abdul Jalil, who leads the National Transitional Council (NTC), said the ultimatum applied to loyalists of Col Muammar Gaddafi in his hometown of Sirte and in other towns.
The announcement came after Col Gaddafi's wife and three of his adult children fled to neighbouring Algeria.
Algeria has defended the move, which rebels called an "act of aggression".
Col Gaddafi's own whereabouts are unknown.
In Libya, rebels are trying to overcome pockets of resistance by Gaddafi loyalists, and preparing to advance on Sirte.
Speaking at a news conference in Benghazi, Mr Jalil said that if there was no "peaceful indication" by Saturday that Gaddafi-loyalists intended to surrender, "we will decide this manner militarily".
"We do not wish to do so but we cannot wait longer," he said.
Mr Jalil also said he had spoken to Nato officials and that the NTC had decided no foreign troops were needed in Libya to maintain security.
"We are betting on our youths and we are certain our bet will pay off," he said.
Battle fears
The rebels made an attempt to reach Sirte last week but were fought back by loyalist troops. On Monday, fighters coming from Benghazi in the east captured the small town of Nofilia, on the road to Sirte.
The BBC's Jon Leyne in Benghazi says the rebels have mainly been negotiating with tribal leaders both in Sirte and the other two main remaining Gaddafi strongholds of Bani Waled, southeast of Tripoli, and Sabha, deep in the Sahara desert region.
While they have had some success with the tribal leaders there has been little response from regime loyalists, says our correspondent, and there are fears that a military assault on Sirte could be a lengthy and bloody battle.
Algeria has said Col Gaddafi's wife Safia, daughter Aisha and sons Muhammad and Hannibal crossed the border between Libya and Algeria at 0845 local time (0745 GMT) on Monday.
The Algerian government later said Aisha Gaddafi had given birth to a daughter shortly after arriving in the country.
The NTC has condemned Algeria, which has not yet officially recognised the council, for offering shelter to the family, calling it "an act of aggression against the Libyan people and against the wishes of the Libyan people".
Mr Jalil said he believed Algeria would not host the family for long before they left for a third country.
"We ask the Algerian government (to ensure) that the presence of those people does not pose a threat to Libya and we hope they will be handed over when they are sought by justice," the AFP news agency quoted him as saying.
Algeria's ambassador to the UN, Mourad Benmehidi, told the BBC earlier that in the desert regions there was a "holy rule of hospitality" and his country had accepted the family on humanitarian grounds.
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