Poles will vote for a new president on Sunday in a tight election that will have major consequences for the future of the country’s pro-EU government.

Opinion polls say Warsaw’s liberal mayor Rafal Trzaskowski and national conservative historian Karol Nawrocki are running neck and neck.

Poland’s president is a largely ceremonial role, but it does come with significant negative power.

The president has the right to veto legislation, and the coalition government lacks a big enough parliamentary majority to overturn it.

Karol Nawrocki is a staunch opponent of Donald Tusk’s coalition, and he is expected to use the veto as much if not more frequently than the incumbent conservative President Andrzej Duda, who cannot run for a third consecutive term.

Tusk has been unable to deliver many of his campaign promises since taking office 18 months ago due to Duda’s veto and divisions within his coalition which includes conservatives, centrists and leftists.

Tusk promised Polish women legal abortion up to the 12th week of pregnancy and voters he would repair the rule of law in the judiciary.

Many critics say Poland’s top courts were politicised under the previous Law and Justice-led (PiS) government that lost power in late 2023.

On both issues, Tusk has made little headway.

After narrowly winning the election’s first round on 18 May, Rafal Trzaskowski pledged to co-operate with the government to accomplish both.

Whichever candidate mobilises their voters in Sunday’s second round run-off will be key to who becomes the next president.

Another significant factor is who can attract the votes of two far-right candidates who placed third and fourth in the first round.

The anti-establishment candidates received three times as many votes as they did in the last presidential election in 2020.

While those voters support Nawrocki’s socially conservative views, some libertarians disagree with his support for generous state benefits for the less well-off.

Both candidates led large, rival patriotic marches in Warsaw last Sunday to show who had the biggest support.

Almost all the participants at Nawrocki’s rally carried the red-and-white Polish flag. No-one had the blue EU flag. One banner read “Enough of Tusk’s [demolition] of democracy”.

Magdalena and her sister Marta said Nawrocki’s patriotism was important. “We care first for our family, then the nation and after that the world,” Magdalena told me.

“A lot of politicians say, ‘Oh, we can’t do that because what will the Germans think about us?’ Sorry, I don’t care what they think,” she said.

Karol Nawrocki, 42, is head of the Institute of National Remembrance, a state body that investigates crimes dating back to the communist era and World War Two. He was relatively unknown nationally before he was picked by PiS to run.

According to the CBOS polling company, voters view him as someone who supports traditional Catholic values and stands up for average Poles, including small farmers who consider themselves threatened by the EU’s Green Deal limiting the use of chemicals and greenhouse gases.

His typical voter is seen as aged over 40, conservative and family-oriented and living in the countryside or small towns and cities.

Previously he was director of the Museum of the Second World War in Gdansk where he changed the exhibition to emphasise Polish heroism and suffering during the conflict.

A keen amateur footballer and boxer, he likes to publish images of himself working out on social media.

His strongman image has been pushed by Polish and foreign politicians alike. Ex-PM Mateusz Morawiecki posting a mock-up of Nawrocki as a Polish Captain America on social media.

Supporter Magdalena said he wasn’t particularly charismatic, but Poland needed “a strong man who will be stable when he’s pushed by the world”.

Earlier this week, US Homeland Security Secretary Kristi Noem flew to a Conservative Political Action Conference (CPAC) in Poland to endorse him as a “strong leader” like President Donald Trump.

“I just had the opportunity to meet with Karol and listen, he needs to be the next president of Poland,” she said five days ahead of the vote.

Noem said his rival Trzaskowski was “an absolute train wreck of a leader”.

Nawrocki’s campaign has been bedevilled by revelations from his relatively unknown past, although so far the allegations appear not to have damaged his support.

He does not deny taking part in football hooligan brawls, and has called them “noble fights”. But in that he is not alone, as several years ago Donald Tusk spoke of taking part in similar fights as a young man.

However he has strongly denied a series of other allegations – that he had links with gangsters and neo-Nazis; that he took advantage of an ill senior citizen to acquire his council flat at a huge discount; and that he helped arrange prostitutes for guests at the luxury Grand Hotel in the seaside resort of Sopot when he worked there as a security guard.

Nawrocki has said he will donate the flat to charity and threatened to sue the news website that published the prostitute story because it was a “pack of lies”.

Many of his supporters think the the stories were made up by the mainstream media, which they see as largely pro-Trzaskowski.

Shaking off the revelations, Nawrocki posted a video on social media set to an old Chumbawamba song, with the chorus, “I get knocked down, but I get up again”.

Trzaskowski’s supporters have been more inclined to believe the allegations, with one man in Warsaw holding a banner reading: “No to the gangster”.

The son of a famous jazz pianist, the 53-year-old mayor of Warsaw is deputy leader of Donald Tusk’s centrist Civic Platform party.

He also speaks multiple languages and once served as Europe minister.

He was joined in last Sunday’s march in Warsaw by another liberal mayor who won the Romanian presidency earlier this month. Nicusur Dan told supporters they shared the same values of a united and strong European Union.

According to CBOS, Trzaskowski’s typical voter is in his 30s, fairly well-off and lives in a city. Voters see him as having left-liberal views supporting LGBT and migrants’ rights.

While his opponents see Trzaskowski as part of Poland’s privileged elite, supporter Malgorzata, a statistician, told me he was “an intelligent, professional European. That’s enough to be a president of Poland”.

Against a backdrop of war in neighbouring Ukraine and the Tusk government’s tough stance against illegal migration, Trzaskowski has portrayed himself, artificially according to some voters, as a man who believes in a strong nation state and patriotism.

Another supporter, Bartosz, said he wanted Poland to remain safely anchored in Europe.

“We know history. In 1939, we counted on Britain and France, but nobody came. If we are partners with Europe politically and economically, then it’s in their interests to support us,” he said.