Official government data showed the center-left grouping leading with 33 seats after 64% of the vote was counted, on top of 20 secured in the first round in the 141-member assembly.
This puts the Social Democrats (SD) ahead of the ruling Homeland Union party which led in six constituencies in addition to 18 first-round wins.
Gabrielius Landsbergis, leader of the Homeland Union, conceded his party’s defeat and congratulated the opposition, saying: “My wish for them [opposition] is to form a responsible government and to have a responsible approach.”
The Baltic country of 2.9 million people has a hybrid voting system in which half of parliament is elected by popular vote. The remainder is decided in district-based run-off votes between the top two candidates, a process that favors the larger parties.
If the SD succeed in forming a government, they are expected to maintain Lithuania’s hawkish stance against Russia and hefty defense spending.
Lithuania will spend about 3% of GDP on its armed forces this year, according to NATO estimates, making it the military alliance’s sixth-biggest spender.
Full results are expected at about midnight (2200 GMT).
The SD won 20% of the vote in the first round on October 13, making it the largest party ahead of the ruling Homeland Union with 18% and the anti-establishment Nemunas Dawn with 15%.
Coalition support weakened by inflation concerns
Prime Minister Ingrida Šimonytė’s center-right three-party coalition has seen its popularity eroded by inflation that topped 20% two years ago, deteriorating public services and a widening rich-poor gap.
After the first round, SD leader Vilija Blinkevičiūtė said she was already in talks about forming a majority coalition government with two other parties - For Lithuania, and the Farmers and Greens Union.
The SD made a pact with opposition parties to support all run-off candidates in contests against Šimonytė’s Homeland Union nominees.
Election shaped by economy and security
Domestic economic issues were in focus during the election campaign, with the SD vowing to tackle increased inequality by raising taxes on wealthier Lithuanians to help fund more spending on healthcare and social support.
But national security is also a major concern in Lithuania, which lies on the eastern flank of NATO and the European Union and shares a border with the Russian exclave of Kaliningrad and Belarus, a close Moscow ally.
Three-quarters of Lithuanians think Russia could attack their country in the near future, a Baltijos Tyrimai/ELTA opinion poll found in May.
