* Libya freed militants turned over by Algeria--govt source
* Says anti-Qaeda fight key to good bilateral ties
* Libya rebel military spokesman scorns the conditions
ALGIERS, Aug 25 (Reuters) - Algeria will not yet recognise Libyan rebels as the new leadership of its neighbour state and wants them to make a strong commitment to fighting al Qaeda in North Africa, an Algerian government source told Reuters.
That message, which drew swift criticism from the Libyan rebel leadership, underscored a degree of tension between Algeria and some Libyan rebel leaders who before Muammar Gaddafi apparent fall in an insurgent advance into Tripoli this week accused Algiers of supporting him in the civil war. Algerian authorities have denied this. [ID:nLDE7222FW]
The high-ranking source also said Algeria, a U.S. ally in the campaign against al Qaeda, has evidence that Libyan militants it had handed over to Gaddafi's government are now at large in Libya and some have joined the insurgents.
"There is proof that Libyan Islamists who were delivered by Algeria to Tripoli have managed to flee and join the rebels. We even saw one of them on Al Jazeera television, speaking in the name of the NTC," said the source, referring to the rebels' National Transitional Council.
"We want to be certain that the new rulers in Libya are involved in the fight against al Qaeda in our region -- this is key for good relations," added the source, speaking on condition of anonymity.
Libya's rebel military spokesman, Ahmed Bani, said Algeria's comments were unfair: "Let them (Algeria) fight al Qaeda first before they impose conditions upon us."
Bani said earlier this week that an estimated "95 percent of Libya is under rebel control". But scattered pockets of loyalist diehards battled opposition fighters hunting for Gaddafi and his sons.
FEARS QAEDA THRIVING IN LIBYAN CHAOS
Algeria has said it believes the chaos inside Libya, and large quantities of weapons circulating there, are being exploited by al Qaeda's North African branch, al Qaeda in the Islamic Maghreb (AQIM).
The NTC has rejected assertions that it has been infiltrated by al Qaeda or other Islamist militants.
Algeria expects an apology from the rebels over their allegation that it supported Gaddafi in the conflict, the government source said.
"Algeria does not recognise the NTC as it is a transitional institution as its name indicates. Because of this we will only recognise the legitimate representatives of the Libyan people once they themselves pick their leaders," said the source.
"Algeria hopes the new Libyan authorities respect treaties and conventions between the two countries, notably on security."
Algeria, a major energy exporter, is still recovering from nearly two decades of conflict between security forces and Islamist militant groups that, at its peak in the 1990s, killed an estimated 200,000 people.
More than 30 countries recognise the NTC as the legitimate representative of Libya.
"We do not get involved in the internal affairs of other countries. We were careful at the start of the revolutions in Tunisia and Egypt but later recognised their new governments once the people there made their choices clear," the source said. "It will be the same for Libya."