By Natalia Ojewska and Drew Hinshaw

WARSAW—A presidential contest in Poland on Sunday was too close to call, clocking a higher voter turnout than any election in the country’s modern history, and setting the stage for a likely court showdown between the nationalist incumbent and his liberal challenger.

President Andrzej Duda declared victory and exit polls released after midnight early Monday gave him 51% to his opponent’s 49%. The difference is too small to project a winner, said Ipsos, the market research firm that conducted the poll. Hundreds of thousands of votes cast from abroad were still expected to come in, with the majority of those expected to go to Warsaw mayor and opposition candidate Rafal Trzaskowski.

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