Algeria’s Foreign Ministry said Gaddafi’s wife Safia, his daughter Aisha and his sons Hannibal and Mohammed had entered Algeria on Monday morning.
The development threatened to create a diplomatic rift just as the rebel National Transitional Council (NTC) worked to consolidate its position as Libya’s new government.
An NTC spokesman said the council would seek to extradite the Gaddafis.
A senior rebel officer also said Gaddafi’s son Khamis, a feared military commander, had been killed in a clash outside of Tripoli. The report could not be independently confirmed.
Meanwhile rebel forces converged on Gaddafi’s hometown of Sirte from east and west, intent on seizing one of his last bastions of support either by force or by negotiation.
Gaddafi’s whereabouts have not been known since the rebels captured Tripoli and his 42-year-old rule collapsed a week ago after a six-month uprising backed by NATO and some Arab states.
Algeria’s acceptance of Gaddafi’s wife and offspring 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.