A complete count of votes from Sunday's election had the euroskeptic party winning 39 seats in the 200-seat Finnish legislature, one fewer than the center-left Social Democratic Party that received the most votes.
Finns Party chairman Jussi Halla-aho also received the most votes by far of any candidate who ran for the Eduskunta legislature. Finnish media are suggesting that could put him in the role of kingmaker in the next government.
An elated Halla-aho called it a "day of joy" and said: "I certainly could never have expected a result like this. Honestly speaking, none of us expected this kind of result."
The leader of Finland's center-left Social Democratic Party vowed to focus on climate and social policies after election results indicated his party won the most seats in parliament.
Antti Rinne, a former union leader and former finance minister, celebrated with supporters at an election party in central Helsinki.
He called on them to "take the Finnish society toward a sustainable climate, social and economic policies."
With 99 percent of the votes counted, the Social Democrats appeared to have won 40 seats, just edging out the populist euroskeptic Finns party, which got 39.
Rinne also told them: "I have to make a honest confession: I hoped still for a better result."
Election returns in Finland indicate the Social Democratic Party was the top vote-getter in the country's parliamentary election, trailed closely by the populist euroskeptic Finns Party.
With 90% of ballots counted on Sunday night, the Social Democrats had won 40 seats in the 200-member parliament and the Finns Party 39.
The preliminary returns gave the conservative National Coalition Party 37 seats and the Center Party that was senior partner in the outgoing government 32.
The Finns Party has gained momentum among rural voters and others who find the climate change proposals of other political parties too daunting.
The leader of Finland's center-left Social Democratic Party says he expects the rest of election night in a two-way contest with the conservative National Coalition Party.
Antti Rinne, said Sunday night the Social Democrats held a small lead after most ballots cast in advance were counted: "It's a thrilling situation. It seems to me this will be a race between us and the NCP."
National Coalition Party leader Petteri Orpo predicted that postelection talks on forming the next Finnish government will be difficult because "whoever comes out first will face hard time in working out a government program."
The Social Democratic Party had 18.9% of the uncompleted tally of advance votes and the National Coalition Party wasn't far behind with 17.2%
Early returns from Finland's parliamentary election have the center-left Social Democratic Party in first place and the conservative National Coalition Party not far behind with most of the ballots that were cast in advance already counted.
Initial results from the pool of 1.5 million advance votes, representing 36% of eligible voters, were published minutes after he polls from Sunday's election closed.
The Social Democratic Party had 18.9% percent of advance votes from the uncompleted tally and the National Coalition Party 17.2%.
Outgoing Prime Minister Juha Sipila's Center Party and the populist Finns Party were close with 15.4% and 15.1% respectively.
Officials said some 300,000 advance votes remained uncounted when polls closed at 1700GMT.
The leader of Finland's center-left Social Democratic Party says he hasn't ruled out having the populist Finns Party as a governing coalition partner, but its differing "value base" is an obstacle.
Social Democratic leader Antti Rinne told reporters after voting Sunday in a municipality north of Finland's capital of Helsinki: "I have not closed out the Finns Party. I have said that if we're the first party, we are going to ask all parties the same questions."
Rinne said his values "differ very much" from those of the chairman of the euroskeptic, anti-immigrant Finns, Jussi Halla-aho.
He said" 'That's a big question for me. We need to have a government where there is the same value base."
Polls before the parliamentary election predicted the Social Democrats would place first with voter support of 19%-21%. The polls had the Finns Party coming in second or third with 15%-16% of the vote.
While the debate over climate change has dominated the campaign for Finland's parliamentary election, the populist Finns Party disagrees with other main parties on what measures to take.
Finns Party leader Jussi Halla-aho told reporters at a Helsinki polling station Sunday that "we want a more moderate and sensible climate policy that does not chase industries away from Finland to countries like China."
The Finns Party, which ahead of Sunday's vote has been polling in second place behind the opposition Social Democrats, has been gaining momentum among rural voters and others who find the climate change proposals of other political parties too daunting.
Some of those proposals include boosting the number of electric vehicles, cutting meat consumption through taxes and switching to more vegetarian food in public places like schools.
Greenpeace is calling the parliamentary vote in Finland the "climate election," saying that "never before has climate and the limits of planet Earth been discussed with such seriousness in Finland."
Sunday's vote in the European Union member of 5.5 million people is taking place in a Nordic country that has one-third of its land above the Arctic Circle and where climate policy has emerged as a key election topic.
Voter Sofia Frantsi, 27, an architect from Helsinki, told The Associated Press "for everybody, it's about the climate. It's kind of a climate election."
Greens lawmaker Emma Kari told the AP that "it's clear a vast majority of Finns is hoping the new parliament takes climate action."
Voters were choosing between 2,500 candidates from 19 political parties and movements for the Eduskunta legislature's 200 seats.
Voters in Finland are casting ballots in a parliamentary election after fierce debates over how best to tackle climate change dominated the campaign, even overshadowing topics like reforming the nation's generous welfare model.
Sunday's vote in the European Union member of 5.5 million people is taking place in a Nordic country that has one-third of its territory above the Arctic Circle.
The center-left Social Democratic Party tops a recent poll with 19% support. The populist Finns Party, however, is polling in second place with 16% support and has been gathering momentum among voters who find the climate change sacrifices proposed by other political parties too daunting.
Some 36% of eligible voters have already cast their ballot in advance, choosing between 2,500 candidates from 19 political parties and movements for the Eduskunta legislature's 200 seats.