Polish Prime Minister Beata Szydło suggested that Europe's member states should be given more options, suggesting she will not allow the reelection of the European Council Donald Tusk.
Polish Foreign Minister Witold Waszczykowski said Thursday that Poland will do everything it can to block Tusk's re-election.
EU President Donald Tusk on Wednesday rejected charges from Poland's rightwing government that he has sought to undermine it, on the eve of a vote on his leadership.
Kaczynski and his Law and Justice (PiS) government accuse Tusk of overstepping his mandate by often engaging in Poland's internal affairs, notably when criticising PiS during the opposition's parliamentary stand-off over media freedom in December.
The presidency of the European Council is a prestigious role involving chairing summits, coordinating the work of the member countries and representing the 28 member countries with one voice on the worldwide stage.
Critics said Mrs May risked alienating Poland, a major Brexit ally, if she did not support their candidate Jacek Saryusz-Wolsk.
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Manfred Weber, leader of the EPP, said: "Tusk is the only EPP candidate for president of European Council".
PiS leader Jaroslaw Kaczynski holds Mr Tusk politically responsible for the 2010 plane crash in Russian Federation which killed his twin Lech Kaczynski, and all other 95 people on board.
The clash, rooted in rivalry between Mr Tusk and Jaroslaw Kaczynski, leader of Poland's right-wing ruling party, cast a shadow over efforts to forge a new unity in the European Union as Britain prepares to leave the crumbling bloc. "I will do my best to make the European Union better", Tusk wrote in a tweet.
"There is an overwhelming support for President Tusk's re-election", Joseph Muscat told reporters.
Mr Tusk was Polish prime minister in 2007-2014.
Szydlo first tried to get the other leaders to postpone a decision on Tusk but found no backing. "I don't see how one country could oppose this solution when all the others are in favour", said Hollande as he arrived for the summit, quoted in the Associated Press.
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