"No line of investigation is going to be ruled out," Aznar said after a Cabinet meeting.
He insisted the probe "will soon bear fruit."
Spanish officials initially blamed Basque separatists for Thursday's attacks but then seemed to backtrack after a van with detonators and an Arabic-language cassette with Quranic verses was found in a stolen van outside Madrid.
A shadowy group later claimed responsibility for the bombings in the name of Al Qaeda (search).
An e-mail, signed by the Brigade of Abu Hafs al-Masri and received by the London-based Arabic newspaper Al-Quds al-Arabi, also said the brigade's "death squad" had penetrated "one of the pillars of the crusade alliance, Spain."
"This is part of settling old accounts with Spain, the crusader, and America's ally in its war against Islam," the claim said.
There was no way to verify that the claim did come from Al Qaeda.