Algeria has been accused of "an act of aggression" after Muammar Gaddafi's wife and three children were admitted to the country after fleeing Libya.
Gaddafi's wife Safia, his daughter Aisha and his sons Hannibal and Mohammed entered Algeria from Libya yesterday morning.
The development threatens to create a diplomatic rift just as the rebel National Transitional Council (NTC) works to consolidate its position as Libya's new government.
Amid reports that Algeria would close part of its border with Libya, an NTC spokesman said the council would seek to extradite the Gaddafis.
"By Saturday, if there are no peaceful indications for implementing this, we will decide this matter 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 this afternoon.
Muammar Gaddafi's whereabouts have not been known since the rebels captured Tripoli a week ago.
Algeria's acceptance of Gaddafi's wife and children angered the rebel leadership, who want him and his entourage to face justice for years of repressive rule and who fear that he could orchestrate a new insurgency unless he is captured.
"We have promised to provide a just trial to all those criminals and therefore we consider this an act of aggression," spokesman Mahmoud Shamman told Reuters. "We are warning anybody not to shelter Gaddafi and his sons. We are going after them ... to find them and arrest them.
"We have heard that Algeria will harbour them till they go to another country. They are trying to go to another country, possibly an east European country," he said.
NTC chairman Mustafa Abdel Jalil called on the Algerian government - which has not recognised the council as Libya's legitimate authority - to co-operate with it and hand over any of Gaddafi's sons on its wanted list.
The Alergian government has said Col Gaddafi's daughter Aisha gave birth to a baby girl the day after arriving in the country.
It said the family was allowed into Algeria on humanitarian grounds and were not on the International Criminal Court's wanted list.
Ultimatum for Gaddafi forces
Meanwhile, Mr Abdel Jalil has given Gaddafi's forces a four-day deadline to surrender towns they still control or face a bloody end to the war.
He said: "By Saturday, if there are no peaceful indications for implementing this, we will decide this matter militarily. We do not wish to do so but we cannot wait longer."
The NTC said today that the war has so far claimed the lives of 50,000 people.
Anti-Gaddafi forces have converged on the coastal city Sirte from east and west.
However, they have stopped short of an all-out assault in the hope of arranging a negotiated surrender of Gaddafi's birthplace.
