The minority United Left party said one reason for the move is the poor example the king has been setting during a time of economic hardship, The Telegraph of Britain reported.
Increased calls for King Juan Carlos, 74, to abdicate follow an elephant hunting trip to Botswana where he injured his hip in a fall.
Tomas Gomez, leader of the Madrid branch of the opposition socialist party, said the king must choose between service and "an abdication that would allow him to enjoy a different kind of life."
The socialist party said it will present a list of questions to Parliament calling for details of the financing of the Botswana trip to be made public.
So far the royal household has declined to give details on the trip except to say that it was a "private matter."