Duda, of the governing Law and Justice (PiS) party, is expected to come out on top in the first-round vote with 41.8 percent, according to an exit poll by Ipsos.
President Andrzej Duda, a 48-year-old conservative backed by the nationalist ruling Law and Justice party, was running against 10 other candidates as he sought a second 5-year term.
His rival Rafał Trzaskowski, representing the Civic Platform opposition party, received 30.4% of the votes, local media reported.
But the poll shows Mr Duda short of the 50% required for an outright win in the first round and, if it is confirmed by official results, he will face Warsaw mayor Rafal Trzaskowski in a run-off on July 12. He also won the backing of US President Donald Trump earlier this week, who said he was doing a "terrific job".
Poland's state electoral commission announced the results of the election on Monday morning based on a count of 99.78% of all votes. "After these five years many more people voted for me".
Originally scheduled for May, the ballot was postponed due to the pandemic and a new hybrid system of postal and conventional voting was in place on Sunday in a bid to stop the election from causing a spike in infections.
"The campaign goes on because Poland needs it", Duda told jubilant supporters in the central town of Lowicz.
That kind of rhetoric - along with the judicial overhaul and the party's harnessing of public media to promote the government's image - have raised concerns among some that Poland is following Hungary in eroding democratic norms established after communism collapsed three decades ago.
Other presidential candidates include Szymon Holownia, a TV personality and journalist who had once studied to be a priest. "For democracy, the judiciary and respect for minorities", said Joanna Ugniewska, 66, after casting her ballot at a polling station in a school in Warsaw city center.
As of Sunday, Poland had almost 34,000 confirmed cases of COVID-19 among its 38 million people, with over 1,400 deaths.
A former EU emissary for his party, Trzaskowski has promised to work towards repairing relations with Poland's European allies, and to oppose any government efforts to tighten already restrictive abortion rules.
Under PiS, Poland became the only European Union state to refuse to commit to the bloc's 2050 climate goal in December 2019, which critics said could undermine its ambition to take on the leading role in the global fight with climate change.
Duda has promised to defend the governing party's raft of popular social benefits, including a child allowance and extra pension payments - a key factor behind the populists winning a second term in October's parliamentary election.
But defeat could see its influence unravel and trigger early elections.
Duda has also echoed PiS attacks on LGBT+ rights and Western values.
Trzaskowski instead supported gay rights and said he is open to the idea of same-sex civil partnerships.
Campaigning with the slogan "Enough is Enough", Trzaskowski has promised a different Poland, although many see his PO party as weak and ineffectual.
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