On social media, he says it is time to "create the conditions for holding presidential elections" and to give the people a chance "for change."
The call comes about five months after Delcy Rodríguez took power as interim president, following a US military attack on the capital Caracas and the removal of President Nicolás Maduro.
76-year-old González Urrutia, a former diplomat living in exile in Spain, was seen by many international observers as the rightful winner in the 2024 presidential election.
The US government has recognized Rodríguez as the new leader, normalized diplomatic ties, eased sanctions and negotiated oil deals. Neither Washington nor Caracas has indicated that any elections are in the offing.
