Official results published on Monday showed that pro-European centrist Rafał Trzaskowski, Warsaw's mayor and candidate for Tusk's Civic Coalition, secured 31.36 percent of the vote.
He was narrowly followed by Karol Nawrocki, supported by the rigt-wing populist Law and Justice party (PiS), who received 29.54 percent.
PM Tusk urges voters to choose 'order over chaos' ahead of presidential runoff
On Monday afternoon, Tusk posted a video message on social media, thanking voters for their participation in the first round of Poland's presidential election and calling on them to make a decisive choice in the upcoming runoff on June 1.
"Do you support paralysis and chaos in Poland, or progress and security?" Tusk asked. "Do you want infighting at the top while war rages beyond our borders, or effective leadership and national strength? Do you prefer impunity and corruption, or justice and order?"
He said that "the only honest answer is Rafał Trzaskowski," clearly endorsing the centrist candidate ahead of the second-round vote.
Polish vote highlights divide between pro-EU liberals and Trump-style conservatives
As The Guardian notes, Piotr Buras, head of the Warsaw office of the European Council on Foreign Relations, told the Associated Press: "The campaign in the next two weeks will be very polarising and brutal - a confrontation of two visions of Poland: pro-EU, liberal and progressive versus nationalist, Trumpist and conservative."
According to Polish experts, including political scientist Aleksander Smolar, the outcome of the second round of the presidential election is expected to remain uncertain until the last moment.
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Source: The Guardian/AP/PAP/X/@donaldtusk