Madrid (CNN) -- Spanish Interior Minister Antonio Camacho warned Friday that although the Basque separatist group ETA has declared an end to violence, the most difficult task still lies ahead -- ensuring no Spaniards suffer the threat of terror attacks in the future.
His remarks come a day after ETA announced a "definitive cessation of its armed activity" in a statement published on the website of Gara, a newspaper the group has used to convey messages in the past.
ETA is blamed for hundreds of deaths in its decades-long fight for an independent Basque state that it wants carved out of sections of northern Spain and southwestern France.
Speaking Friday on Spanish National Television, Camacho said: "We have completed a first part of our task, (but) there remains the more complex one, guaranteeing through the strict enforcement of our laws that never again will any generation of Spaniards have to suffer on their backs the weight of a barbarity that slows down our progress and compromises our future."
He said ETA had been defeated "by the tireless and unstoppable work of the police and the civil guard" and that as a result it had been forced to declare an end to violence without achieving a single one of its aims.
The security services had achieved that outcome "with tenacity, with work, with dedication, and above all, with a lot of suffering," he said.
U.S. National Security Council spokesman Tommy Vietor said Friday that ETA's announcement "holds out the prospect of a historic step toward peace, although there is a long road ahead to realize this promise."
He paid tribute to the victims of ETA violence, adding: "We recognize the courage of the Spanish government and the Spanish people in their enduring efforts to advance democracy and freedom in Spain and around the world."
"The Spanish people have endured over 40 years of violence at the hands of ETA," said the spokesman for U.N. Secretary-General Ban Ki-moon. "The secretary-general shares in the hope that ETA is committed to bringing this tragic chapter for Spain to an end."
European Commission President Jose Manuel Barroso hailed the development as "a truly historic moment which ends years of terror and attacks on Spanish society."
The news "marks the culmination of years of unceasing efforts in the fight against terrorism," he said, congratulating Spain on its efforts to combat ETA.
Police have cracked down in recent years on ETA in Spain and France, leaving it operationally weak.
There have been numerous statements from the Basque group calling for talks or a peace process of some sort, but all falling short of declaring a definitive end to violence.
The Spanish government said that since ETA has broken cease-fires in the past; only an authoritative statement that it is putting down its arms for good will do.
Thursday's announcement followed a recent push for the group to abandon violence permanently. That effort was led by international figures who include Sinn Fein leader Gerry Adams of Northern Ireland and former U.N. Secretary-General Kofi Annan.
In a nationally televised address hours after the announcement was posted, Spanish Prime Minister Jose Luis Rodriguez Zapatero termed ETA's announcement as being of "transcendental importance" and a "victory for democracy."
"Ours will be a democracy without terrorism, but not without memory," Zapatero said, referring to 829 people killed by ETA and their families.
The prime minister praised Spanish police, Civil Guard personnel, the intelligence agency and judicial authorities "who have contributed to this end." Zapatero also singled out France -- which has traditionally been used as a rearguard base for ETA -- and its president, Nicolas Sarkozy, for their assistance.
The prime minister said that it would be up to Spain's next government -- which will be formed after parliamentary elections on November 20 -- to lead the peace process.
In remarks Thursday night at their respective political party headquarters in Madrid, the two main contenders to replace Zapatero -- Alfredo Perez Rubalcaba, the candidate from Zapatero's Socialist Party, and Mariano Rajoy, leader of the opposition People's Party -- cheered the development but did not detail what they would do next if they were to become prime minister.
In its statement Thursday, ETA -- which is listed as a terrorist organization by Spain, the United States and the European Union -- outlined why now was the right time to make such a declaration.
"A new political time is emerging in the Basque Country," ETA said. "We have a historic opportunity to find a just and democratic solution for the centuries-old political conflict."
The group then added that "dialogue and agreement" should predominate "over violence and repression."
ETA urged the Spanish and French governments to conduct "direct dialogue" aimed at addressing outstanding issues while calling upon fellow Basques to commit to such a process.
CNN's Al Goodman and Mariano Castillo contributed to this report.
Liam Fox, Britain's defense minister leaving the Ministry of Defence building on October 13. 