"I feel sympathy for the King," said the famous director during a press conference in Los Angeles to present his new film, the comedy I'm So Excited.
"He has always been very nice with me so I don't want to cause him any problems," the Oscar-winning director told journalists gathered in a Beverly Hills hotel.
"But I think we should have the possibility of a referendum to ask the Spanish people what they think about the system and ask if they want a constitutional monarchy or not."
The comments came up in the context of a joke in the Spanish director's latest film about the alleged infidelities of Spain's King Juan Carlos.
Spain's King has been repeatedly linked in recent times to German princess Corinna zu Sayn Wittgenstein. Spanish media have described the two as "good friends".
"(The film) is a comedy," said the director from Spain's Castille–La Mancha region.
"Everybody is thinking and talking about these things in relation to the King and whether he has had romantic liaisons with other people.
"I thought this was a good moment to include the joke," he added.
Almodóvar told journalists that the perception of Spain's Royal Family had changed in recent years, especially in the wake of the publication of Pilar Urbano's book by Queen Sofia, La reina muy de cerca.
"That book shocked me," the gay director said on Tuesday.
"For me it was awful to find all these homophobic statements about gay marriage. I felt frustrated," he explained.
"Then came all the corruption around the Royal Family. Five years ago the problem was taboo in Spain. Nobody dared to talk about it," said the director,
"But now it's' on the street every day."
Spain's Royal Family has seen its popularity fall in recent times, largely because of a high profile corruption case involving the King Juan Carlos' son-in-law, Iñaki Urdangarin.
Urdangarin — married to the King's second oldest daughter, the Infanta Cristina — is currently being investigated for his possible involvement in the diversion of funds from the charitable sports foundation, the Nóos institute.
Cristina is also in the firing line. A judge in Palma de Mallorca also demanded on May 24th that the tax authorities provide him with a report on Cristina's property and non-property assets, investment funds, financial assets and deposits, a copy of the order showed.
A poll run by Spain's left-wing El País newspaper in April showed that 53 percent of people surveyed disapproved of the way the 75-year-old King Juan Carlos was carrying out his functions, against 42 percent who approved.
That gave him an overall approval-versus-disapproval rating of -11, compared to +21 in December, a lower rating than the one received by tax inspectors or lawyers and the first time that he has received a negative rating.
Felipe's approval ratings have also taken a hit but remain broadly favourable.
A majority of Spaniards, 61 percent, approve of Felipe against 33 percent who disapprove, giving him an overall approval-versus-disapproval rating of +28, compared to +37 in December.