WARSAW, July 12 (Xinhua) -- Poland's incumbent president Andrzej Duda was ahead by a tiny margin in Sunday's presidential run-off, showed an Ipsos exit poll.

According to Ipsos, Duda, who is supported by the ruling Law and Justice (PiS) party, received 50.4 percent of the vote, while his rival, Rafal Trzaskowski -- backed by the main opposition party Civic Platform (PO) -- won 49.6 percent.

With margins well within the two percentage point margin of error, the race is too close to call until at least partial results come in, with a distinct possibility that a winner can only be pointed out after all ballots are counted.

According to the Polish Press Agency, under the State Electoral Commission's optimistic scenario, the official results of the presidential run-off could come late on Monday or in the night from Monday to Tuesday. Otherwise, the final results will be announced by 11 p.m. (2100 GMT) on Tuesday.

Poles voting abroad will likely be a major factor in the final outcome. Over 500,000 ballots were cast outside of Poland, but are not reflected in the exit polls.

Speaking in the town of Pultusk, Duda claimed victory and invited Trzaskowski and his wife to the presidential palace to finish the campaign "with a handshake."

Trzaskowski also told his crowd in Warsaw that he is absolutely confident he will prevail. "All that needs to be done is to count the votes."

Ipsos, the polling company that conducted the exit polls for the three major news networks in the country, meanwhile announced that no winner can be declared at this point.

According to Ipsos, the election turnout reached 68.9 percent, surpassing the record set during the presidential elections of 1995, at 68.2 percent.