Key Eurocrat Donald Tusk has vowed to "make the European Union better" after he was confirmed for a second term as its Council president.
Polish Foreign Minister Witold Waszczykowski said Thursday that Poland will do everything it can to block Tusk's re-election.
Asked about how Poland as a recipient of European Union funds could try to block the summit's conclusions, Szydlo said it was the right of every member country to reject the document if that was beneficial for its national interest.
Critics said Mrs May risked alienating Poland, a major Brexit ally, if she did not support their candidate Jacek Saryusz-Wolsk.
The Prime Minister will attend the first day of the European Council summit in Brussels on Thursday for talks on migration, security and economic growth.
In Brussels, the PM is not expected to discuss Brexit and has no bilateral meetings arranged with other leaders, but will stress that the United Kingdom is a strong advocate of the EU's free trade agenda, and wants to see strong economic growth in the bloc.
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The government in Warsaw argues that the decision should be delayed because of its displeasure with Tusk, a bitter political rival. "We can not hide this, this country is Germany", Kaczynski told reporters in Warsaw.
Diplomats from several member nations say Warsaw has little or no support, while Tusk has strong backing.
Tweeting from his personal account, Tusk wrote in Polish: "Thank you for holding thumbs and heartfelt support".
Muscat this afternoon chaired the session during which Tusk was reconfirmed at the helm of the European Council.
Tusk is expected to be backed by an overwhelming majority of leaders. "The EU will remain engaged in the Western Balkans and stand by its commitments", Tusk said.
European Commission's Future of Europe White Paper, unveiled last week by its President Jean-Claude Juncker, will be debated as national leaders need to find a common position for the future direction of the European project ahead of the Rome summit.