No official ceremony was held in the country, now a constitutional democracy with a Socialist government.
The service on Sunday was held at the Valley of the Fallen (Valle de los Caidos) and marked the anniversary of the execution in 1936 of Jose Antonio Primo de Rivera, the founder in 1933 of the Falange, the party that provided the ideological basis for the government of Franco, who is buried in the basilica in the valley.
Another demonstration took place in Madrid, called by an association of former Franco-supporting combatants from the 1936-39 civil war that ended with the defeat of the republican side and the victory of Franco.
Franco's death, after almost four decades in power, saw the restoration of the monarchy, which enjoys wide but declining support, with the young in particular tempted by republicanism.
Diehard Franco supporters crowded the basilica of Santa Cruz del Valle de los Caidos, where Franco is buried, on Saturday night for a Roman Catholic Mass in his memory.
Patrimonio Nacional, the national heritage agency responsible for the basilica, built by republican prisoners, said that 6000 people filled the church and that hundreds more who could not squeeze in remained outside.
In Madrid, demonstrators
marched for national unity
The ceremony was organised by the Francisco Franco Foundation, and witnesses said it was attended by the late dictator's daughter, Carmen Franco Polo, and by ex-Civil Guard Lieutenant Colonel Antonio Tejero, who sought to overthrow the democratic government by seizing parliament on 23 February, 1981.
At the end of the Mass, several hundred people remained behind chanting fascist songs and yelling insults against the government led by Prime Minister Jose Luis Rodriguez Zapatero.
In central Madrid, between 1500 people - according to the police - and 8000 - the demonstrators' count - marched on Sunday in support of "national unity", responding to an appeal from the Falange.
On Saturday night, several hundred anti-Franco demonstrators marched in the city centre, waving republican and anarchist flags.