Foreign Minister Witold Waszczykowski said Poland would “do everything” to prevent a vote on the matter.
Correspondents say such hostility among compatriots is highly unusual in EU politics.
German Chancellor Angela Merkel has backed a new 30-month term for Mr Tusk, saying it would be a “sign of stability”.
As European Council president, he would play a major role in the UK’s Brexit negotiations.
What is Poland doing?
Poland’s government is desperately trying to prevent Mr Tusk from being re-elected to a second term as president of the European Council. Instead it has proposed its own candidate, a little-known Polish MEP called Jacek Saryusz-Wolski.
“We will inform our partners that the whole summit is threatened if they push to force a vote today,” he told the broadcaster TVN24.
PM Beata Szydlo has also written a letter to EU leaders saying Mr Tusk has “violated multiple times his European mandate” by getting involved in Polish political disputes and supporting the opposition to the government.
The EU has angered Poland’s nationalist government by criticising changes to the country’s top court, new restrictions on journalists and its opposition to resettling refugees by quota.
Why is the Polish government so hostile to Mr Tusk?
Mr Tusk was prime minister from 2007-2014. He led the centre-right Civic Platform when the PiS was in opposition.
The plane crashed in dense fog. Official investigations ruled pilot error was the principal cause.
In 2012, Jaroslaw Kaczynski told Mr Tusk in parliament: “In the political sense you bear 100% responsibility for the catastrophe in Smolensk.”
Jaroslaw Kaczynski also accused Mr Tusk of favouring “solutions that are extremely harmful to Poland”.
What does the European Council president do?
The European Council brings together the heads of state and government of the 28 EU member states. Jointly they set the EU’s strategic direction in key areas, such as reform of the eurozone, the Greek debt crisis, the migrant challenge and relations with Russia.
Mr Tusk took charge in late 2014 and his term ends on 31 May. If his fellow leaders back him on Thursday, he will stay in office until 30 November 2019. That period coincides with the expected two-year Brexit talks on UK withdrawal from the EU.
Malta, currently chairing EU business, is likely to seek approval of Mr Tusk by consensus. Poland’s hostility may push it to a vote – but then Mr Tusk is still likely to win by a qualified majority.