Three masked Eta members read out a statement on Saturday night at a pro-Eta rally saying the group "confirms its commitment to continue to fight... until independence and socialism for the Basque country is won," local media reported.
"The fight is not a thing of the past. It is the present and the future," the group said.
Jose Luis Rodriguez Zapatero, Spain's prime minister, said in a speech on Sunday that Eta and its supporters should reject violence and "engage in politics and nothing more than politics".
Eta has been fighting a bitter battle for a separate Basque homeland for more than 40 years, killing more than 800 people. It announced its ceasefire in March this year.
In June, Zapatero told Spanish parliament that he was prepared to negotiate with Eta, but only on the issues of the organisation's dissolution and the fate of Eta prisoners in Spanish jails.
He was not prepared to offer concessions regarding possible Basque independence and talks have since stalled.
The conservative opposition has accused Zapatero of caving in to what it calls an active terrorist group because Eta has neither disarmed, renounced violence nor shown repentance.
Meanwhile, since late August there has been a renewal of urban violence in the Spanish Basque country, with radical ETA sympathisers blamed for burning buses and throwing Molotov cocktails.
Batasuna, Eta's banned political wing, has said it believes that the peace process is currently in a "particularly serious situation".