Batasuna is considered Eta's political wing, though there is no formal link and the remarks appeared to be evidence of a split between them.
Batasuna's leader, Arnaldo Otegi, said at a press conference on Monday in the Basque city of San Sebastian: "We want to call on Eta to keep to the commitments and objectives it set in its statement of March 22."
Eta then called a truce to "drive the democratic process in the Basque Country".
Güncelleme Tarihi: 20 Eylül 2018, 18:16
The group has not officially claimed responsibility for the bomb, which ripped apart a car park at Barajas airport on December 30, but one of the warning calls was made in the group's name.
The separatists did not make a formal statement breaking the ceasefire, as they have done on previous occasions, and Batasuna officials in recent days expressed surprise at the attack.
Analysts have since speculated that the bomb may have been planted by a splinter group.
Batasuna has distanced itself from Eta's attacks but has stopped short of condemning its violence, a prerequisite for the party to be made legal and take part in elections again.
The Spanish prime minister, Jose Luis Rodriguez Zapatero, met the conservative opposition leader, Mariano Rajoy, on Monday to discuss the political fallout from the recent bombing.
The Popular party has consistently opposed the government's policy of fostering a dialogue with Eta, and has been critical of it since the blast.
Batasuna and Eta have long fought for independence for the Basque Country, seven provinces in northern Spain and southwest France.
Eta began its violent campaign under Franco's dictatorship when Basque language and culture were supressed.
The Spanish part of the Basque Country, made up of three of the seven provinces, now has a degree of autonomy.
Since the airport bomb, the Madrid government has called an end to the Basque peace process, and police in the northern region have found more stashes of explosives.