Financial Times reported Sunday evening a TVN television poll showed Komorowski captured 45.7 percent of the vote to 33.2 percent for Jaroslaw Kaczynski, the brother of President Lech Kaczynski, who died along with his wife and dozens of others in an April 10 plane crash near Smolensk in western Russia.
A separate national television poll indicated Komorowski received 40.7 percent to Kaczynski's 35.9 percent, the Times said.
The runoff will be July 4.
"Both in football and in politics, the hardest is the shootout," Komorowski told supporters after polls closed. "Let's mobilize and fight for a better future for Poland."
Speaking to supporters, Kaczynski said: "We have to win for our country. These are elections which are the result of a great tragedy."
Komorowski ran as a liberal candidate with the ruling centrist Civic Platform, Kaczynski, the conservative Law and Justice party.
Conservatives lost a parliamentary election in 2007 and have turned to Kaczynski's veto powers to block liberal policy moves.
The election came as Poland tried to clean up after being deluged with floods in recent weeks that have killed 24 people and forced thousands to leave their homes.