Demonstrations were held in about 40 cities across Spain in protest actions called by leftist groups. In Madrid organisers said 15,000 people participated, however, the police said the number was about 4,000.
Similar demonstrations were held in Barcelona, Valencia, Bilbao, Oviedo and other Spanish cities. The demonstrators demanded a referendum on whether Spain should continue as a monarchy or become a republic.
The United Left (IU), the third most powerful force in the Spanish Parliament, are eying the possibility of a referendum that would call for state reform. IU leader Cayo Lara said a bill would be introduced in parliament seeking a referendum in the next three months.
The effort, however, is seen as having little chance because of the ruling conservative People's Party (PP) and most members of the opposition socialist party defend the monarchy.
King Juan Carlos, 76, made his surprise announcement on Monday, clearing the way for Crown Prince Felipe, 46, to become the country's next king.
Spain's legislature must pass special legislation to allow the announced abdication because the country's laws do not currently allow for abdication.
The palace has said it expects the crown prince to be coronated as Felipe VI within three to six weeks.
Spain's monarchy was installed by former dictator Francisco Franco. Juan Carlos has sat on the throne since 1975.