A report carried on Spain's public-service radio says arrests were made in the Madrid and Barcelona areas and in the Basque region.
No officials were immediately available for comment.
Those arrested reportedly included the imam of a mosque. One suspect is thought to be linked to an attack on an Italian military police base in southern Iraq.
Suicide bombers devastated the Italian base in November 2003, killing 18 Italians and nine Iraqis.
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