The Platform for a Truth Commission called on political parties ahead of Spain's general election on December 20 to commit to investigating disappearances during the 1939-1975 of Francisco Franco.
UN experts have urged Spain to break a decades-long taboo by investigating alleged crimes of the 1936-39 civil war and the Franco dictatorship that followed.
"We ask all the parties to commit once and for all to fulfilling the UN resolutions during the next legislature," the movement's spokesman Jordi Gordon told AFP.
The aim is to "set up a parliamentary truth commission to recognise the victims of Franco and establish the facts".
With the 40th anniversary of his death looming on November 20, Franco remains a divisive figure in Spain.
During the transition to democracy after his death in 1975, Spanish leaders agreed an amnesty for the crimes of the past four decades so that the country could move forward.
But critics say the atrocities were too serious to be covered by an amnesty.
The platform estimates there are at least 150,000 unsolved "disappearances" and some 2,380 mass graves that have never been exhumed, Gordon said.
It also demands an official investigation into how babies were taken away from their mothers during the dictatorship.
It announced its latest campaign for a truth commission on Friday and formally launched it at an event in Madrid on Saturday.
Spain's former Socialist government in 2007 passed a "historical memory law" that was supposed to shed light on Franco-era crimes.
But Gordon said a "victims' bureau" set up under that law had been suppressed by the conservative government that took power in 2011.