With a third of ballots counted, the Central Electoral Committee said early on Monday that the liberal Civic Platform Party led the polls with 41.1% of the vote, while the Law and Justice Party trailed with 31.63%.
"We have suffered a defeat," Kaczynski said. "I congratulate Donald Tusk."
Tusk, who heads the current opposition, has promised an "economic miracle" in the country, a complete withdrawal of Polish troops from Iraq, tax cuts, and to attract back the vast number of Poles who have left the country to work in wealthier Western European states.
Kaczynski, 58, who has led Poland for two years with his twin brother Lech, the country's president, remains popular among the older generation. However, the leader of the ruling Law and Justice Party has lost some support over his aggressive attitude to Russia, his backing of U.S. missile shield plans, his conservative Catholic stance on social issues, and perceived lack of progress in tackling official corruption.
Kaczynski said after acknowledging defeat that a coalition with the winner of Sunday's election was inconceivable and that he would form a new opposition.
The Central European country showed a 52.6 percent voter turnout on Sunday, higher than any parliamentary elections in Poland since the fall of communism in 1989.
Commenting on the early results of the election, a senior Russian lawmaker said the success of the opposition in Poland would lead to serious changes in the country's domestic and foreign policy.
"The focus on narrowly-defined nationalistic interests will shift to collective efforts, both inside the EU and NATO, and indirectly in relation to Russia," said Konstantin Kosachev, who
heads the International Affairs Committee of the lower house of Russia's parliament, the State Duma.
