Portugal's prime minister, whose rightist coalition won a general election in March, said on Sunday he would back former center-left Socialist premier Antonio Costa if he decides to run for the European Council top job.

The Council, which represents national governments of the 27 member states, is one of the European Union's three main political institutions, along with the European Commission and the European Parliament.

The rise of euro-skeptic nationalist parties in this Sunday's European Parliament election might complicate Ursula von der Leyen's bid for a second term as president of the Commission, though she remains the front-runner for the job.

If von der Leyen is reelected, the Council presidency is likely to go to the Socialists, and Costa, who governed Portugal for eight years since the end of 2015 but stepped down in November last year, is widely seen as a strong candidate.

The current European Council president is Charles Michel, who will helm the institution until the end of November this year.

"It is possible the presidency of the European Council will go to a Socialist candidate," Portugal Prime Minister Luis Montenegro said. "If Antonio Costa is a candidate for this position... the Portuguese government will not only support (him) but will do everything to ensure his candidacy is successful."

Montenegro made the comments as he reacted to the results of the European Parliament election, which in Portugal was won by the Socialists by a narrow margin with 32.1% of the vote, slightly above Montenegro's ruling Democratic Alliance (AD) coalition.