Donald Tusk was also re-appointed as president of the European Council Summit for the same period.
Prime Minister Joseph Muscat of Malta, which holds the European Union rotating presidency, said Poland decided that "politically irrespective of the contents of the conclusions, to veto, or at least not agree with any of the conclusions".
The attack on Tusk, made in a letter to governments of the 28-member bloc, came a day ahead of a Brussels summit where leaders were expected to rubberstamp a new two-year mandate for the former Polish premier.
After being confirmed as president again, he tweeted: "Grateful for trust & positive assessment by #EUCO (European Council)".
Most of the 28 European Union leaders had hoped to push through Polish ex-premier Tusk's re-election with a minimum of fuss so they could concentrate on other challenges.
European Commission President Jean-Claude Juncker, left, speaks with European Council President Donald Tusk as they wait for the start of a pre-EU summit Tripartite meeting at the Europa building in Brussels on Wednesday, March 8, 2017.
The leaders of the big four governments in the EU27 gathered at the Palace of Versailles on Monday, and agreed that some European Union countries could deepen integration faster than others.
"We want to know what kind of blackmail or pressure was used to vote against our candidate", Waszczykowski said, referring to MEP Jacek Saryusz-Wolski whom Warsaw had officially proposed to replace Tusk.
"I prepared my beloved quotation: "Be careful of the bridges you burn because once they are gone you can never cross them again", he said.
The president chairs summits of the 28-nation bloc's leaders.
The PiS government strongly opposed the reappointment of Tusk, who is closely tied with the centrist opposition in Poland.
The hostilities between Kaczynski and Tusk are said ot be personal, as Kaczynski holds Tusk "morally responsible" for his twin brothers death in a 2010 plane crash over Russian Federation. "There are very clear rules of engagement and rules of procedure that we will follow", Muscat said.
One unnamed German official said that Chancellor Angela Merkel appreciates Tusks work, and believes he will be re-elected with "overwhelming support".