APS did not say when the Libyans were arrested.
Their capture, in the capital Algiers, was made possible by information provided by a former member of the group who had surrendered to the authorities on May 1.
The Libyan fighters, aged between 22 and 25, had been "recruited in Libya by extremist networks with international ramifications", APS said.
Al-Qaeda in the Islamic Maghreb, previously known as the Salafist Group for Preaching and Combat, or GSPC, claimed responsibility for the April 11 triple suicide bombings of the prime minister's office and a police station in Algiers that killed 33 people and wounded 57 others.
The attacks were the deadliest in the region since 2002, and came as the North African nation struggles to come to terms with an uprising that has killed up to 200,000 people since 1992, but which has largely died down in recent years.
According to media reports, Algerian security forces have arrested an unspecified number of suspects accused of "logistical preparations" for the attacks, and some of them have already reportedly been brought before prosecutors.
On Tuesday, al-Qaeda in the Islamic Maghreb said it would carry out more suicide bombings and urged Muslims to join its ranks as suicide bombers.
Al Jazeera aired a video from the organisation purportedly showing how one of the April 11 bomb attacks was carried out.
The brief video showed what appeared to be landmines and explosives being put together, followed by a large explosion.
At the end of the aired segment, a bearded man said to be Abu Musab Abdulwadood, the leader of Algeria's main Islamic movement, called on young Muslims to join his group, join the "long list of martyrs" and carry out suicide bombings.
Security officials suspect the group is attracting growing numbers of Muslim youths in the region and providing them with military training.
In late December Algerian newspapers reported that security forces had arrested two Tunisians "belonging to an international terrorist network".