Spain's Supreme Court has ruled that the government must ask Argentina to extradite 39 former military officers for alleged human rights violations.
Some 30,000 people may have been killed during the 'dirty war'
It said the refusal by Spain's former conservative government to seek the extradition of the officers and also one civilian had been against the law.
Among the men is Jorge Videla - one of the heads of the military council that ruled Argentina between 1976 and 1983.
Spanish law allows trials for crimes against humanity committed abroad.
The Spanish Supreme Court overturned the decision by the country's former cabinet several weeks ago but made its ruling public only on Friday.
It said the current Socialist government of Jose Luis Rodriguez Zapatero "must hand over these extradition requests to the Argentine government through diplomatic channels".
One of Spain's top investigating judges, Baltasar Garzon, has repeatedly demanded the prosecution of the 40 Argentines.
Human rights groups say up to 30,000 political opponents were kidnapped, detained and later executed during those years - also known as Argentina's "dirty war".
In April, a former Argentine naval officer was convicted in Spain of crimes against humanity and given 640 years in prison.
Adolfo Scilingo, 58, was found by a court to have been on board planes from which 30 people were thrown to their deaths during the military rule.
Scilingo volunteered to go to Spain in 1997 to testify about atrocities that took place under the right-wing regimes in Argentina and also Chile.
His lawyer said Scilingo was a scapegoat and that he would appeal.