By Adrianna Ebert and Karol Badohal

WARSAW (Reuters) -Polish liberals performed worse than expected in a presidential election on Sunday, an exit poll showed, as Rafal Trzaskowski from ruling centrists Civic Coalition (KO) scraped to victory setting up a close fight for Warsaw's pro-European path.

Trzaskowski placed first with 30.8% of the vote, ahead of Karol Nawrocki, the candidate backed by the nationalist Law and Justice (PiS) party, who had 29.1%, according to an Ipsos exit poll. The gap was much narrower than the 4-7 percentage points seen in opinion polls before the vote.

If confirmed, the result would mean that Trzaskowski and Nawrocki will go head-to-head in a runoff vote on June 1 to determine whether Poland sticks firmly on the pro-European track set by Polish Prime Minister Donald Tusk or moves closer to nationalist admirers of U.S. President Donald Trump.

"We are going for victory. I said that it would be close and it is close," Trzaskowski told supporters. "There is a lot, a lot, of work ahead of us and we need determination."

Nawrocki also told supporters he was confident of victory in the second round and called on the far-right to get behind him and "save Poland."

"We have to win these elections so that there is no monopoly of power of one political group, so that there is no monolithic power in Poland," he said.

An Opinia24 poll for private broadcaster TVN published after the first round gave Trzaskowski 46% in the run-off and Nawrocki 44%, with 10% of voters either undecided or refusing to say.

Far-right candidates Slawomir Mentzen and Grzegorz Braun scored almost 22% combined, a historically high score.

Braun, who in 2023 used a fire extinguisher to put out Hanukkah candles in the country's parliament, an incident that caused international outrage, won 6.2% of the vote according to the exit poll.

Mentzen stopped short of immediately endorsing Nawrocki.

"Voters... are not sacks of potatoes, they are not thrown from one place to another," he said. "Each of our voters is a conscious, intelligent person and will make their own decision."

Stanley Bill, Professor of Polish Studies at the University of Cambridge, said the combined strong showing of nationalist and far-right parties meant the results were "a disappointment for the Trzaskowski camp and put wind in the sails of Nawrocki."

"I would add to this that the results are a significant blow to Donald Tusk's ruling coalition," Bill added. "Candidates representing parties that won 53.7% of the vote in the 2023 parliamentary elections won only 44.9% of the vote this evening."

Turnout was 66.8% according to the exit poll.

The vote in Poland took place on the same day as a presidential run-off vote in Romania, in which centrist Bucharest mayor, Nicusor Dan, appeared on course to defeat Eurosceptic hard-right lawmaker George Simion.

PRESIDENTIAL VETO

In Poland, the president has the power to veto laws. A Trzaskowski victory in the second round would enable Tusk's government to implement an agenda that includes rolling back judicial reforms introduced by PiS that critics say undermined the independence of the courts.

However, if Nawrocki wins, the impasse that has existed since Tusk became prime minister in 2023 would be set to continue. Until now, PiS-ally President Andrzej Duda has stymied Tusk's efforts.

If the exit poll is confirmed, the other candidates in the first round, including Mentzen from the far-right Confederation Party, Parliament Speaker Szymon Holownia of the centre-right Poland 2050 and Magdalena Biejat from the Left, will be eliminated.

Two updated polls that take into account partial official results will be published later in the evening and early on Monday morning.

ROLE IN EUROPE

Trzaskowski has pledged to cement Poland's role as a major player at the heart of European policymaking and work with the government to roll back PiS's judicial changes.

Nawrocki's campaign was rocked by allegations, which he denies, that he deceived an elderly man into selling him a flat in return for a promise of care he did not provide. But Trump showed support by meeting Nawrocki in the White House.

Nawrocki casts the election as a chance to stop Tusk achieving unchecked power and push back against liberal values represented by Trzaskowski, who as Warsaw mayor was a patron of LGBT marches and took down Christian crosses from public buildings.

Unlike some other eurosceptics in central Europe, Nawrocki supports military aid to help Ukraine fend off Russia. However, he has tapped into anti-Ukrainian sentiment among some Poles weary of an influx of refugees from their neighbour.

He has said Polish citizens should get priority in public services and criticised Kyiv's attitude to exhumations of the remains of Poles killed by Ukrainian nationalists during World War Two.

(Reporting by Adrianna Ebert, Kuba Stezycki and Fatos Bytyci in Gdansk, Pawel Florkiewicz, Anna Wlodarczak-Semczuk, Anna Koper, Marek Strzelecki, Barbara Erling, Janis Laizans and Thomas Holdstock in Warsaw, writing by Alan Charlish; editing by Barbara Lewis, Philippa Fletcher, Aidan C. Lewis, Rod Nickel and Diane Craft)