With only 38 percent of the vote, exit polls show Tusk is shy of the 50 percent needed, forcing a runoff election Oct. 23, the Scotsman reports.
The two leading candidates are Tusk and Lech Kaczynski of the Law and Justice Party, who got 32 percent.
Both parties are center-right and won heavily in parliamentary elections held two weeks ago.
Outgoing President Aleksander Kwasniewski cannot run again after serving two five-year terms.
His government of ex-communists is accused of corruption and the leading presidential candidates are pledging "moral change" in the government.