Libyan rebels fighting against the remnants of Colonel Gaddafi's regime have given his forces until Saturday to surrender.
The leader of the interim National Transitional Council (NTC), Mustafa Abdul Jalil, said on Tuesday that unless he received a "peaceful indication" that Gaddafi's forces would lay down their arms then the NTC would "decide this manner militarily".
"We do not wish to do so but we cannot wait longer," he said through a translator at a press conference in Benghazi.
The announcement came as NTC military commander Hisham Buhagiar claimed that 50,000 people had been killed in Libya since the start of the uprising there six months ago.
Algeria closed parts of its long stretching border with Libya on Tuesday, the local El Watan newspaper reported after the interim Libyan government condemned the Algerian authorities for accepting the ousted dictator's relatives.
The NTC may seek extradition to bring the Gaddafi family to justice, it has also been reported.
"Especially for Hannibal, if he fled to Algiers and the Algerian authorities allowed him to do that, we'll consider this as an agressive act against the Libyan people's wish," Mahmoud Shammam, NTC information minister, said.
"We're going to use all the means to get him back and try him, put him in a court and try him. This is our aim. We would give everybody of the Gaddafi family a fair trial and we can guarantee that."
But Algeria's envoy to the United Nations defended the decision to take in the Gaddafis saying it was a "holy rule of hospitality" to provide assistance.
Mourad Benmehidi told the BBC World Service that his nation had a duty to provide assistance.
"In fact in many parts of the Sahara region it's mandatory by law to provide assistance to anyone in the desert," he told the broadcaster.
Relations between Algeria and the NTC were strained before the Gaddafi family fled. The NTC previously accused Algeria of sending mercenaries to fight for Gaddafi, while Algeria's autocratic regime has resisted calls to recognise the legitimacy of the NTC and repressed protests within its own country.
Elsewhere in Libya senior rebel commanders reported that another of Gaddafi's sons, Khamis, had been killed.
"We have almost certain information that Khamis Gaddafi and Abdullah al-Senussi (his intelligence chief) were killed on Saturday by a unit of the national liberation army during clashes in Tarhouna," spokesman Ahmed Bani told Al Arabiya television.
Khamis Gaddafi has been reported dead twice before since the uprisings began earlier this year, however, and the deaths remain unconfirmed.
Meanwhile fighting in Libya on Tuesday was focused mainly around Gaddafi's hometown of Sirte, where it has been rumoured that the dictator may be hiding.
Nato said that it hit 35 targets in airstrikes on Monday, including four radar sites and 22 armed vehicles in Sirte alone.
An ammunition storage facility and two command centres near to Bani Walid were also hit, as were five anti-aircraft artillery sites and other military installations close to Hun.
Sky News reporter Neal Mann said via Twitter that Nato jets were also seen in the skies above the north African nation on Tuesday.
In other parts of the country the Libyan people were working to recover from the fighting. In Tripoli, fireworks replaced celebratory gunfire in Martyrs' Square on Monday evening.
Children were photographed trying to rebuild and clean their residential streets, while a memorial wall was built remember those who have died in the fighting, according to footage posted on YouTube.
A document was also leaked that appeared to document plans by the United Nations to leave up to 200 military observers and 190 police on the ground to help shore-up Libya's post-conflict recovery.
In another sign of the growing, though fragile, stability in the capital, the UK Foreign Office has said that it is working to reestablish an embassy there as a reflection of recent "progress".