Acting Prime Minister Pedro Sánchez has headed a caretaker government with reduced powers since a July 23rd general election produced a hung parliament, in which a ruling majority cannot easily be formed.
While his Socialist party finished second behind the conservative Popular Party (PP), it is better positioned as it has more potential partners.
Sánchez is trying to win an investiture vote in parliament - which determines who forms the government - with the support of its far-left partner Sumar and smaller regional parties, including Catalonia's separatists.
The coalition last week elected the Socialist party's candidate for parliamentary speaker, the third-highest office in Spain after the king and the prime minister.
But PP leader Alberto Núñez Feijóo argues that since his party won the most seats - 137 of the 350 in parliament - he should be asked by the king to form a government.
Even with the backing of far-right party Vox, the PP will still fall short of the 176 votes needed to pass an investiture vote.
Felix Bolanos, a minister in Sánchez's cabinet, said Sunday that it would be a "waste of time" for Feijóo to present himself in an investiture vote since it is impossible for him to secure enough support to pass.
The king began the talks on Monday with smaller parties and will meet the main party leaders on Tuesday, finishing with Feijóo.
The king traditionally has invited the winner of the most seats to form a government, but he can opt for other leaders if it appears that they are better positioned to provide a stable cabinet.
The nominated party leader must then win an investiture vote to take office. If there is still a deadlock two months after the first vote, the king must call fresh elections.
Comments