The family members include Gaddafi’s wife Safia, his daughter Aisha and his sons Hannibal and Mohammed.
Libya’s National Transitional Council (NTC) chairman Mustafa Jalil implored the Algerian government to extradite Gaddafi’s family members so they could face trial in Libya.
“We have promised to provide a just trial to all those criminals, and therefore we consider this an act of aggression.
“We are warning anybody not to shelter Gaddafi and his sons. We are going after them to find them and arrest them.”
The NTC believe that Algeria will allow the four to travel to another country.
The rebels meanwhile have claimed that another Gaddafi family member Khamis, commander of the country’s elite 32nd Brigade, was killed by a NATO airstrike outside Tripoli.
However, the whereabouts of the fugitive Libyan leader and his son Saif are still unknown.
In other news the US are pushing for the reopening of the Lockerbie case after Libya has stabilised.
The news comes after Lockerbie bomber Abdel Basset al-Megrahi was pictured, apparently on his deathbed in Tripoli.
Al-Megrahi was convicted of killing 270 people when he planted explosives on a Pan Am flight which blew up over Lockerbie, Scotland in 1988.
?Two years ago he was released on compassionate grounds after he was diagnosed with terminal cancer. His release by Scottish authorities caused widespread controversy in the US.