However, with a parliamentary majority already out of reach after the first round of voting, Andrius Kubilius, the party leader, will have to form a working coalition government with a number of parties.
Kubilius, a former prime minister, said: "We are ready to take responsibility and expect the president [to] offer to start forming a new cabinet."
Multi-party coalitions are the norm in Lithuania, which was ruled by the Soviet Union for five decades.
Gediminas Kirkilas, a social democrat and leader of the current centre-left administration, has been at the head of a five-party government since becoming prime minister after a 2006 reshuffle.
The newly-formed Rising Nation party, also known locally as the "showbiz" party because it is led by a popular entertainment television presenter, also did well in the first round, emerging as the second-largest party with around 15 per cent of the vote.
Under Lithuanian law, 70 parliamentarians must be elected by proportional representation from party lists and the remaining 71 in single-member constituencies.
Voter turnout in the first round was higher than expected at 48 per cent, although analysts do not expect the same level of interest in the second round.
Polling stations opened on Sunday at 7am (0500 GMT) and were due to close at 8pm (1800 GMT).
The results are expected to be announced on Monday.