In the first round on May 10, neither Conservative challenger Andrzej Duda nor incumbent Bronislaw Komorowski gained the 50% needed to win outright.
Andrzej Duda edged Bronislaw Komorowski, who had been the favorite and is looking for a second term, by 34.7% to 33.7%.
Poland’s president has limited powers, but is head of the armed forces and can veto new laws.
Bronislaw Komorowski, 62, took office five years ago after his predecessor, Lech Kaczynski, died in a plane crash.
The incumbent president is an independent allied with the centre-right Civic Platform, which has been in government since 2007.
Opinion polls before the first round had put him comfortably in the lead and Bronislaw Komorowski said the result was “a serious warning for the entire team in power”.
Andrezj Duda, 43, is from the right-wing opposition Law and Justice party, which is led by former President Lech Kaczynski’s twin brother, Jaroslaw.
He attracted most support in the more conservative eastern regions of the country, near the border with Ukraine and Belarus.
The presidential vote comes ahead of parliamentary elections this autumn.
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