Spain's leading paper, El Pais, reported on Sunday that a police report released in May said that recruiters for these groups have recently become more active.
The recruiters operate in mosques and aim to radicalise young Muslim immigrants, said El Pais. Some of these mosques are clandestine and operate in parking lots or business premises.
The report also said that Spanish anti-terrorist units have uncovered the presence in Spain of the Moroccan Islamic Combatant Group, Algeria's Salafist Group for Preaching and Combat and Takfir Wal Hijra.
All three organizations, linked to al-Qaeda, have recruited Muslim immigrants, mainly Moroccans, it said.
Police also are keeping an eye on Pakistani extremists and supporters of Lebanon's Hezbollah group, El Pais said.
In the first four months of 2006, Spanish police arrested 31 suspected extremists in six operations, El Pais reported.
However, since the March 11, 2004 bombings on the Madrid commuter rail network that killed 191 people and wounded more than 1,800, police have netted 250 people, of which more than 100 are currently in jail.
A judge overseeing the investigation has said the Madrid cell that carried out the bombings was apparently inspired by al-Qaeda, but had no direct links to it.
Juan del Olmo, the national court's judge, concluded the probe in late June, setting the stage for a trial.