Spanish PM Jose Luis Rodriguez Zapatero has reacted cautiously to the announcement by Basque separatist group Eta of a permanent ceasefire.
Eta's fight for Basque independence has lasted four decades
Mr Zapatero said he was hopeful but any peace process after so many years of horror would be "long and difficult".
Eta is blamed for killing more than 800 people in its four-decade fight for independence for the Basque region of northern Spain and south-west France.
The group says it now wants to promote the "democratic process".
The BBC's Danny Wood, in Madrid, says the ceasefire could be the first step towards a formal peace process.
Eta, which is classed as a terrorist group by the US and the European Union, declared an "indefinite" ceasefire in 1998 but peace talks broke down and the bombing campaign resumed a year later.
The group has never previously called a permanent stop to the violence.
'Joined in hope'
Mr Zapatero has said previously that a permanent end to hostilities by Eta is a condition for any talks.
He said he would take time deciding how to respond to Wednesday's statement.
"Now I trust we will be joined in hope," he added.
But opposition leader Mariano Rajoy said the ceasefire was a pause and it did not amount to a renunciation of criminal activity.
"It does not repent of anything and it does not ask the victims of terrorism for forgiveness," he told Spanish TV.
The declaration was also rejected by Spain's Association of Victims of Terrorism as a "new trick by the murderers to achieve their political objectives".
However, the president of the Basque region, Juan Jose Ibarretxe, welcomed Eta's declaration as an "enormous relief to all of the Basque society".
"It opens a window of hope that nobody should close," he said.
A spokesman for Batasuna, the banned political wing of Eta, called on the governments of Spain and France to help his party join in the political process.
French President Jacques Chirac said Eta's declaration "raises great hopes for Spain and for the fight against terrorism", his office said.
The Eta statement was read out by a woman in a mask wearing a black Basque beret, flanked by two colleagues similarly dressed.
"At the end of this process, Basque citizens will be able to have a voice and the power to decide their future," she said.
1959: Eta founded
1968: Eta kills San Sebastian secret police chief Meliton Manzanas, its first victim
1973: PM Luis Carrero Blanco assassinated
1978: Political wing Herri Batasuna formed
1980: 118 people killed in bloodiest year
Sept 1998: Indefinite ceasefire
Nov 1999: End of ceasefire, followed by more bomb attacks in January and February 2000
Dec 2001: EU declares Eta a terrorist organisation
March 2003: Batasuna banned by Supreme Court
May 2003: Two police killed in Eta's last deadly attack
Nov 2005: 56 alleged Eta activists on trial in the largest prosecution of its kind
March 2006: Eta declares permanent ceasefire
"Ending the conflict, here and now, is possible. This is the desire and the will of Eta."
The ceasefire will come into effect on Friday, the statement said.
The group's activities have been waning, with the number of bombings falling in recent years. The last deadly Eta attack was in May 2003.
Some analysts said Eta's campaign became virtually untenable after the Madrid train bombings in March 2004, blamed on Islamists, caused widespread popular revulsion.
Nearly 200 people died in the series of attacks.
In the 1970s Eta killed scores of people every year, many of them Spanish police, judges and politicians.
There have been several small bombs in recent weeks, but none caused injuries.
The 1998 ceasefire led to a dialogue with the conservative government of Jose Maria Aznar.
But talks broke down in November 1999 and the following year Eta embarked on a renewed bombing campaign.
However, Spanish and French police responded with a wave of arrests which were said to have hit the organisation hard.