The country "cannot afford symbols that separate Spaniards," Pedro Sanchez said in an interview with national broadcaster TVE, adding that the Valley of the Fallen should be converted into "a mausoleum for victims of fascism."
The mausoleum northwest of Madrid was opened in 1959 to house the remains of more than 30,000 Spaniards who fought on both sides of Spain's 1936-39 civil war.
Franco, who led a nationalist-Catholic army against Republican forces during the war, ordered the site to be built as an act of reconciliation and was himself laid to rest there after his death in 1975. The remains of many Republican soldiers were reburied there without their families' permission.
The bill also ordered the creation of a truth commission and the cancellation of politically motivated court rulings during Franco's reign.
The ruling conservative Popular Party under Prime Minister Mariano Rajoy ignored the resolution amid concerns the move would open historical wounds. The Popular Party itself emerged from an earlier party formed by former Franco government officials.
Sanchez's Socialist Party formed a minority government at the beginning of June after ousting Rajoy in a confidence vote. Sanchez is aiming to cement the party's grip on power ahead of a general election due before mid-2020.