The political wing of the Basque separatist group Eta says peace talks with the Spanish government are not over, despite Saturday's bomb blast.
Authorities say it will take days to remove all the wreckage
A Batasuna spokesman, Xabi Larralde, said the peace process "is not broken". The group - outlawed in Spain - gave a news conference in Bayonne, France.
Earlier, Spain's government said peace talks with Eta were now "finished".
The body of an Ecuadorean has been found in the rubble of a multi-storey car park blown up at Madrid's airport.
The victim was named as Carlos Alonso Palate, 35. Another Ecuadorean man was also reported missing after the bomb struck the Barajas airport car park.
Authorities say it will take several days to clear an estimated 40,000 tons of concrete, under which about 400 cars are thought to be buried.
Mr Larralde said the peace process was at a "critical" phase but "our commitment is for it to move forward".
Batasuna has urged Eta militants to explain why they bombed Barajas airport.
"It was not expected by anyone, even though we all knew the [peace] process was in crisis", said Batasuna official Joseba Alvarez, speaking on a Basque radio station.
Eta statement awaited
The government blamed Eta, which called a "permanent" ceasefire nine months ago.
A caller claiming to represent Eta had given a telephone warning just before the explosion.
"Eta has evidently broken off the peace process," Spanish Interior Minister Alfredo Perez Rubalcaba said.
Eta declared a permanent ceasefire on 22 March 2006. The group has been waging an armed campaign for more than 30 years and is blamed for more than 800 deaths.
Eta's last fatal attack was a car bombing in May 2003.
Mr Alvarez accused Spain's Socialist government of failing to take any "concrete steps... to create favourable conditions" for a solution.
But he also said the planting of a bomb without previously announcing the end of a ceasefire was "something new" for Eta.
"It is up to Eta to explain why it acted in that way," he said.