Madrid, Spain (CNN) -- The Basque separatist group ETA's cease-fire statement is insufficient, Spain's interior minister said Monday.
Interior Minister Alfredo Perez Rubalcaba, in the government's first major reaction, said that the statement, released to media Sunday, is "very far from the minimums" that the Spanish government has laid out for the group.
"The word 'truce' as a concept of limited peace to have a dialogue is dead. That's the past," Rubalcaba told Spanish state television TVE.
He said the government's demand remains steadfast -- that ETA agree to unconditionally lay down its arms and end the violence forever, with a process to verify that.
Rubalcaba said security forces would not let up on ETA during its unilateral cease-fire, and he said ETA called the cease-fire at a time of "extreme weakness," due to police crackdowns against the group.
ETA has announced cease-fires before and broken them, notably the 2006 cease-fire that was announced as "permanent," only to be broken months later with a car bomb at Madrid's airport that killed two people.
In a statement published on the website of Basque newspaper Gara on Sunday, ETA -- which is blamed for more than 800 deaths in its long fight for Basque independence in northern Spain and southwest France -- "calls on the Spanish government to agree to the the minimum democratic solutions toward a peace process."
The latest cease-fire announcement was not unexpected, following weeks of calls for a new peace process by some smaller leftist Basque political parties.
The cease-fire announcement also follows months of what is widely regarded as a successful police crackdown against ETA operatives in Spain and also in ETA's hideouts in neighboring France and Portugal.
Police have arrested many of ETA's suspected top operatives, as well as many ETA foot soldiers, and seized bomb-making materials and weapons from hidden arms caches, virtually shutting off ETA attacks.
In its cease-fire announcement Sunday, ETA said that "months ago it decided not to carry out armed offensive actions," but made no mention of what it might consider a "defensive" action.
The announcement was accompanied by an ETA video which showed three apparent ETA members seated at a table in front of an ETA banner.
They wore white hoods covering their faces. The hoods had eye holes, but their mouths were covered.
The person in the middle apeared to do all the speaking in the ancient Basque language -- not in Spanish -- and the voice seemed to be that of a woman.
ETA is listed as a terrorist group by the United States and the European Union for its campaign of car bombings and shootings.
The Spanish government of Prime Minister Jose Luis Rodriguez Zapatero began a peace process in 2006 during the last unilateral ETA cease-fire, but after ETA's airport bomb, the government called off negotiations.
Since then, officials of Zapatero's government have said they would not accept a simple cease-fire statement. Instead, they have said they will accept only a definitive statement from ETA to end its armed fight, and to announce when and where it would lay down its arms forever.
Only then would the government be willing to consider leniency for some of the more than 500 ETA prisoners in jail, officials have said.
The Basque region in northern Spain already has considerable home-rule authority, with its own police, parliament, taxing power and control of health and education. But ETA rejects those as partial steps, and has fought for full independence.
ETA's goal is an independent Basque nation comprising the three-province Basque region and the neighboring Navarra region in Spain, along with three departments in southwest France that also have Basque roots. About three million people live in those areas now.
ETA's cease-fire statement called on the international community to get involved in the Basque peace process.
On Sunday, the leader of the Sinn Fein party in Northern Ireland said he supported the cease-fire.
"Gerry Adams has welcomed ETA cease-fire announcement," the Sinn Fein party said on its Twitter page.
While ETA has announced cease-fires before, the absence of government involvement makes Sunday's statement unique, said Luis Aizpeolea, a correspondent for the Spanish newspaper El Pais. Past announcements have come after back-channel negotiations between government officials and ETA, Aizpeolea said.
But this time, it was smaller leftist Basque political parties that appeared to have pushed ETA to make the cease-fire. The most significant of those parties is Batasuna, which is outlawed because the courts have found it is not independent, but a very part of ETA.
Rubalcaba, Spain's interior minister, said that if Batasuna wants to get back into local politics and run candidates in elections next year, it must either make a full and convincing break from ETA, or convince ETA itself to end its armed struggle.