The government of Prime Minister Pedro Sanchez, which took office last month, has pushed the plans forward.
He said Spain could not allow “symbols that divide” and said the site should be transformed into a “memorial to the victims of fascism”.
But Franco’s descendants oppose the move and Sunday’s protest came after far-right groups called for a “national, patriotic and religious pilgrimage” to prevent what it termed Mr Sanchez’s “plunder” of the grave.
Franco ruled Spain from the end of the country’s civil war in 1939 until his death in 1975. The country embraced democracy in the years that followed.
Hundreds of thousands of people were killed in Spain’s civil war between 1936 and 1939, in which Franco’s Nationalists fought against left-leaning Republicans and Communists supported by the Soviet Union.
Nazi Germany and Mussolini’s Italy were among the countries that provided military support to Franco. Historians have since described the conflict as a dress rehearsal for the Second World War.
