Eta said it did not mean to cause casualties in the blast, accusing the government of failing to evacuate the car park where the bombing took place despite several telephone warnings, Gara reported.
The airport had been largely evacuated, but both victims were sleeping in parked cars.
Eta blamed the Spanish government and the ruling Socialist party for "placing obstacles endlessly in the democratic process", Gara said in a summary of what it called a long Basque-language statement.
Hours before Eta's statement, the government announced the arrest of two suspected Eta members in southern France linked to arms caches found in late December and last week in the Basque region.
|Basques continue to protest for |
They were the first arrests since the Madrid car bombing.
Spain's government has responded to the bombing by scrapping plans for negotiations with Eta and declaring an end to peace negotiations.
The Spanish interior minister, Alfredo Perez Rubalcaba, said he had not immediately read Eta's statement, but said "Eta has only one path left to take, which is to end the violence."
On Monday, Batasuna, a political party banned for its links to Eta, called on the separatists to keep the ceasefire.
In its statement, Eta reiterated a claim that the government had made, and was not keeping, unspecified promises as part of the process that began with the truce, Gara said.
Eta and its political supporters had said in recent months that continued arrests and trials of suspected Eta members were endangering the peace process, which was launched with its announcement in March last year of a "permanent" ceasefire.
The group had also been demanding the transfer of Eta prisoners from jails around Spain to prisons in the Basque region - a move rejected by the government.
Eta wants to promote peace negotiations, but reserves the right to "respond" if what it calls government aggression against the pro-independence movement continues, Gara said.
The separatists said progress in peace talks must come from a "political agreement" that includes "the minimum democratic rights owed to the Basque country".
This was an apparent reference to Basques' long-standing demands to be able to decide between independence and remaining part of Spain.
It called on the government to halt "police formulas and failed policies that lead nowhere", said Gara, which did not publish a full text of the Eta statement.