Sources quoted in the Algerian newspaper Echorouk indicated the government made the decision based on arrest warrants issued by the International Criminal Court for Gadhafi, his son Saif and intelligence chief Abdullah al-Senussi, The Guardian reported.
Moammar Gadhafi has been in hiding.
A former bodyguard for one of Gadhafi's sons said the Libyan leader, ousted from his Tripoli compound by rebels, was moving south via Banki Walid toward Sabha, the route reportedly used by his family members when they fled to Algeria.
The National Transitional Council has called Algeria's decision to accept Gadhafi's wife, daughter Aisha and sons Hannibal and Mohammed "an act of aggression," saying they would seek to extradite the Gadhafi family members.
A team of humanitarian experts the European Union sent to Tripoli is trying to help restore the water supply to the capital cut by Gadhafi forces, The Guardian reported. If efforts to restore the supply fail, the European Union is working on a plan to ship bottled and tanked water to Tripoli, officials said.
"The disruption of the drinking water supply to Tripoli is a major issue affecting the capital's population," an EU spokeswoman said in an e-mail. "Government forces closed the pumping stations … when fleeing from the capital."
NTC leader Mustafa Abdel Jalil announced Tuesday Gadhafi loyalists in the leader's hometown of Sirte have until Saturday to surrender. A buildup of rebel forces has been reported around Sirte, one of a few remaining Gadhafi strongholds, but an all-out attack hasn't started because the NTC is trying to negotiate the town's surrender.
Sky News reported NATO jets were seen flying over Sirte.
Internationally, Zimbabwe ordered Libya's ambassador and staff to leave Harare after Taher Elmagrahi publicly recognized the NTC, al-Jazeera reported Tuesday.
"The Libyan ambassador and his staff are required to leave Zimbabwe within the next 72 hours," Zimbabwean Foreign Minister Simbarashe Mumbengegwi told reporters.
Some Libyan rebels say they are certain Moammar Gadhafi's son, Khamis, and intelligence chief Abdullah al-Senussi are dead, but the deaths were not confirmed.
Rebel military spokesman Ahmed Bani was quoted as saying rebels have information that the younger Gadhafi and Senussi were killed during weekend fighting southeast of Tripoli, The Tripoli Post reported Tuesday.
"Khamis Gadhafi was buried in Bani Walid," Bani reportedly told al-Arabiya.
Jalil said Monday he did not have official information about Khamis' death.
Khamis Gadhafi, leader of the notorious Khamis Brigade, has been reported dead twice before, only to reappear on television.
In The Hague, Netherlands, ICC lead prosecutor Luis Moreno-Ocampo said Monday he may seek an arrest warrant for Khamis Gadhafi, accusing him of crimes against humanity.