Mr Acebes told the parliamentary commission of inquiry into the 11 March attacks that there had been no sign of an Islamic link until two days later.
He also pressed for the "reach of Eta's shadow" to still be investigated.
Mr Acebes, whose party was ousted in general elections three days after the blasts, insisted he had told the truth.
He said that after the attacks, which killed 191 people, his government had acted with "maximum transparency" but others had launched an election strategy to pour scorn on the government and take advantage of the situation.
Mr Acebes, the first former government minister to give evidence, has been criticised at the commission hearings for jumping to blame Basque militants Eta in the wake of the attacks.
'No alternative'
Critics have suggested that the Popular Party government rushed to blame Eta out of fear that an al-Qaeda link - and its implications of retaliation for Spain's support for the war in Iraq - could cost it the general election.
An Islamic group with links to al-Qaeda is now blamed for the attack. Most of those suspected to have been involved are Moroccan.
Mr Acebes told the hearing on Wednesday that there was no suggestion of an alternative to Eta, although it was already known that the dynamite used was not one favoured by the Basque militants and that an Arabic tape was found in a car abandoned by the plotters.
He said he gave no credibility to declarations rejecting a Basque link to the attacks from Eta and the banned Basque political party Batasuna hours after the bombings.
Mr Acebes said it was not until 13 March - after the first arrests and a claim of responsibility - that there was a significant suggestion of an Islamic terror link.
The former interior minister also called on the new government to continue the investigations into the attacks and possible links with Eta. He said the pieces still "didn't fit".
He said it was still necessary to find out who "designed the attacks, who planned the sequence of events, especially the day and hour of claiming responsibility" for the attack the afternoon before the 14 March general elections.
The commission has the job of establishing whether more could have been done to prevent the bombings, and of assessing what impact they had on the 14 March election.
Former Foreign Minister Ana Palacio is due to appear before the commission later on Wednesday.