Spain is "entering a new political cycle," Alberto Núñez Feijoo, leader of the main right-wing opposition party, the People's Party (PP), said on Tuesday after his victory in local and regional elections.

The victory of Fajoo's PP against Prime Minister Pedro Sanchez's Spanish Socialist Workers' Party (PSOE) represents "a first step towards entering a new political cycle that we will find in the coming months," the opposition leader said, referring to the parliamentary elections to be held at the end of the year.

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Fajoo addressed the crowded supporters from the balcony of the PP headquarters in central Madrid, standing alongside two of the big winners of the day: Madrid regional government prime minister Isabel Díaz Ayuso and capital José Mayor Luis Martínez Almeida, both triumphantly re-elected with an absolute majority of votes.

"My time will come if the Spaniards ask for it," Feijoo said in response to cheers who already see him as the next prime minister.

"We won emphatically and democratically," Feihoo said.

"We have achieved an outstanding result everywhere" in the country, he added against the backdrop of cheers.

Socialist Prime Minister Sanchez did not comment on the election results last night, AFP reported.