The Spanish Interior Ministry confirmed the identity of the pair arrested Saturday as Oier Gomez Mielgo and Itziar Moreno, El Pais reported Monday.
Moreno is suspected of being involved in a car bomb attack against regional television and radio offices in Bilbao.
Gomez Mielgo is accused of overseeing a bomb-making facility in Portugal for the armed Basque nationalist organization ETA.
Since ETA declared a cease-fire in January, the Basque radical separatist group Bildu attempted to run in the local elections in May.
The Spanish courts publicly rejected ETA violence after a previous party, Sortu, was declared illegal.
"If they want the disappearance of all violence, particularly ETA's, as their charter stated, Sortu need to join the democrats and demand that the terrorist group disappear indefinitely," said the Basque chief of interior affairs, Rodolfo Ares.
Bildu leaders rejected the incident.