WARSAW — In the race to govern Poland, Prime Minister Donald Tusk appeared to have a strong lead on Sunday over his conservative rival and predecessor, Jaroslaw Kaczynski, while a party that supports gay rights, abortion and some drug legalization seemed set to win representation in Parliament for the first time.

Though final results are not expected until Tuesday, Mr. Tusk claimed victory late Sunday and Mr. Kaczynski conceded defeat after exit polls reported on state television indicated that Mr. Tusk’s centrist Civic Platform was receiving nearly 40 percent of the vote and Mr. Kaczynski’s Law and Justice Party just over 30 percent. Hours later, preliminary returns from 15 percent of the nation’s polling places showed Mr. Tusk’s party leading, 37 percent to 30 percent.

If the results hold, it will be the first time since the fall of Communism that any party in Poland has won consecutive parliamentary elections. The election was widely watched because of concerns over Mr. Kaczynski’s confrontational approach toward the European Union.

Analysts hailed the vote for continuity as a sign of political maturity in Poland, another step in the democratic development of the largest of the Eastern European countries to join Western institutions like the NATO alliance and the European Union.