The final confirmed election results will be announced on April 17.
The Finns Party won 39 of the 200 seats in the parliament, more than double its pre-election strength.
The latest opinion polls had indicated that the Social Democrats stood an excellent chance of becoming the country's largest party, thus securing the post of Prime Minister, although it was widely recognised that they would obtain less than 20 per cent of the vote.
Outgoing Prime Minister Juha Sipila said his Centre Party was the election's "biggest loser", blaming the "difficult economic decisions" his administration made in an attempt to rebalance the economy after a long slump. "Everybody's feeling some kind of a depression about it", voter Sofia Frantsi, 27, an interior architect from Helsinki, told The Associated Press on Sunday.
The Finns' strong showing further complicates coalition talks, with most party leaders ruling out any cooperation with them.
The election followed a campaign in which concerns about climate change even overshadowed the issue of how to reform the nation's generous welfare model.
Finnish governments are typically a coalition of three or four parties that form the minimum 101-seat majority in parliament.
In Finland, polling is underway for general elections.
Some have blamed the shrinking lead on the inability of party leader Antti Rinne, a 56-year-old former trade union boss, to attract large numbers of new, younger voters.
More than 1.5 million people - 34.5 per cent of the total - voted in advance of the parliamentary elections on Sunday under a system put in place in 1970 to encourage participation.
Only 0.2 percentage points separated the two parties - in a heavily splintered political landscape where the Social Democrats were the biggest party with 17.7 per cent of votes. Most political parties support government actions to curb global warming.
Meanwhile, the Finns Party, which won 39 seats, had focused nearly entirely on an anti-immigration agenda under the leadership of hardline MEP Jussi Halla-aho, who also decried the "climate hysteria" of the other parties.
"Finland isn't capable of saving the world", Jussi Halla-aho, 47, said at one of the party's news conferences.
"Rinne has been pretty clear that there are substantial ideological differences between the Social Democrats and the Finns Party".
In all, Finnish voters chose from nearly 2,500 candidates from 19 parties. The populist Finns Party, however, is polling in second place with 16 percent support and has been gathering momentum among voters who find the climate change sacrifices proposed by other political parties too daunting.
Reform has been controversial in Finland and plans to cut costs and boost efficiency have stalled for years, leaving older voters anxious about the future.