Polls show the party ending up in second or third place, meaning it could play a significant role in the next government, which in Finland is typically a coalition of three or four parties. Much of the debate in the run-up to the election has been about whether the next government should continue the current administration's public spending cuts.
"There have been a lot of cuts and some, like education, in areas they promised they wouldn´t cut".
Rinne on Sunday announced he will send all other parties a list of questions, including ones about values, to decide which parties to invite to the coalition formation talks.
Social Democrat leader Antti Rinne could become Finland's first leftist prime minister in two decades.
However, in a tacit acknowledgement that the public mood was against further belt-tightening, Orpo has insisted that the economy is now strong enough to allow for some more generous public spending.
Voter turnout of 72 percent was higher than the 70.1 percent who voted in 2015.More news: Zion Williamson Becomes First Duke Freshman to Win Wooden Award
A record 1.5 million Finns, over a third of the electorate, had already cast their ballots during a week of advance voting earlier this month. On Sunday, queues were reported at some polling stations in the capital.
Chairman of the Finns Party Jussi Halla-aho, right, campaigns for the Finnish parliamentary elections in Tuusula, Finland, Saturday, April 13, 2019, a day ahead of the elections. The victors, led by Antti Rinne, 56, a former trade union chief, won 40 seats opposing the austerity of the previous centre-right government.
The nationalist True Finns party came in fourth, with 15.1% of the vote.
The anti-immigration Finns Party also decries the "climate hysteria" of other parties seeking action against global warming.
Finns Party leader Halla-aho has sought to dispel accusations that he hoped to keep his party in opposition after the election, so as to avoid facing the tough decisions of being in power.
Last month Prime Minister Sipila dissolved his cabinet after failing to steer through parliament a long-fought plan to reform the country's health and social care system.More news: Masters 2019: Bettor wins $1.19 million on Tiger Woods' green jacket win
Forecasts suggest no party is likely to draw more than 20 percent of the vote, meaning the result could be historically close. "Negotiations for a new government will be very tough and very hard", Social Democrat supporter Mikko Heinikoski, 37, said.
The major parties have all expressed strong reservations about joining a government with the Finns Party, whose policies lurched to the right after Halla-aho became leader in 2017.
"For the first time since 1999 we are the largest party in Finland ..."
In January, outrage over highly publicised reports of a string of alleged sexual assaults by foreign men led to a surge in support for the Finns Party, who have pledged to drastically cut immigration and tighten asylum rules.
The Finns party's stance on environmental policies, which includes an opposition to a proposed tax on meat consumption, appeals to rural voters in particular who fear soaring fuel costs and resent any efforts to change what they see as the traditional Finnish way of life. Polls close at 8:00 pm (1700 GMT) with all votes expected to be counted by midnight.More news: Giuliani: Going to See 'No Collusion' From Mueller Report