Bronislaw Komorowski, Poland's centrist presidential candidate, faces a tight run-off vote against his right-wing rival Jaroslaw Kaczynski on July 4 after beating him by only a few percentage points in Sunday's election.
Results from 94 per cent of the polling stations showed no single candidate had won enough votes to win outright, with Komorowski on 41 per cent against 37 per cent for Kaczynski.
Financial markets would prefer a Komorowski victory because he would be expected to work smoothly with the economically liberal government of Donald Tusk, the prime minister, in tackling a big budget deficit and preparing to join the euro.
But first-round results gave the mild-mannered candidate of Poland's ruling pro-business Civic Platform a narrower margin of victory than many pre-election polls had suggested.
Nazanine Moshiri, Al Jazeera's correspondent in Warsaw, said: "The race here is still very much wide open."
Speaking to Al Jazeera, Dariusz Rosiak, a Polish journalist, said: "He [Kaczynski] will try to get as much support as he can from ... the left wing voters who voted over 13 per cent for their candidate.
"It will be a clash for these two candidates [Kaczynski and Komorowski], for the votes of this part of the electorate.
Kaczynski is a conservative politician ... but to a large extent the main theme of his politics is solidarity, he will appeal to the social conscience of the voters, he will say 'I will protect the less well off people in this country'."
Kaczynski, a combative nationalist, is vying to replace his twin brother Lech Kaczynski, whose death in a plane crash in Russia in April forced the early election.
Komorowski, the speaker of parliament and the country's acting president, shares Tusk's vision of a Poland firmly anchored in the European mainstream.
He favours working closely with Germany and other EU partners and trying to improve long troubled ties with Russia,
Kaczynski is opposed to joining the euro any time soon and is distrustful of the EU, Russia and Germany.
While the prime minister holds most of the power in Poland, the president can veto laws, appoint key officials and also has a say in foreign and security policy.