The text put forward by the main opposition Socialists was passed with 198 votes in favour and one against.
Approval of the motion is symbolic since it does not place any obligation on the government to act, but it has reopened debate over the massive Valley of the Fallen mausoleum some 50 kilometres (30 miles) northwest of the Spanish capital.
The text put forward by the main opposition Socialists was passed with 198 votes in favour and one against. The ruling conservative Popular Party (PP), which was founded by former members of the Franco regime and which lacks a majority in the 350-seat assembly, abstained.
Franco governed Spain with an iron fist from the end of Spain's 1936-39 civil war and his death in 1975, when he was buried inside a basilica drilled into the side of a mountain at the Valley of the Fallen.
Built by Franco's regime between 1940 and 1958 in the granite mountains of the Sierra de Guadarrama, the monument holds the remains of over 30,000 dead from both sides in the civil war.
The dictator, whose Nationalist forces defeated the Republicans in the civil war, dedicated the site to "all the fallen" of the conflict in an attempt at reconciliation, but the monument was built in part by the forced labour of political prisoners, many of whom died during the works.
The mausoleum features a giant stone cross and other symbols of Franco's National-Catholic ideology, and is seen by many as a relic of the dictatorship.
Families of those killed in the civil war complain that the man who ruled as a fascist dictator for nearly four decades should not lie in a monument to victims of the conflict that brought him to power.
The motion approved by parliament calls for the mausoleum to be "given a new meaning" so it is no longer "a place of Francoist memory" and instead favours reconciliation.
The text also called for the remains of Jose Antonio Primo de Rivera, founder of Spain's fascist Falange party who died during the civil war, to be moved from the basilica in the Valley of the Fallen to a less prominent spot at the site.