He called on them to "take the Finnish society toward a sustainable climate, social and economic policies".
In the parliament resulting from the 2015 legislative vote, the Center Party had held 49 seats after garnering more than 21 percent of the vote. Preliminary results are expected later Sunday night.
The opposition Social Democratic Party has vowed to alleviate the austerity policies introduced by the ruling coalition over the past four years.
Antti Rinne's close victory will make negotiations to form a governing coalition particularly hard, not least because the major parties have all expressed strong reservations about joining a government with the Finns Party, whose policies took a further lurch to the right after Halla-aho became leader in 2017. He may approach the National Coalition party, which won 38 seats.
Opinion polls suggest the Social Democrats' lead has narrowed in recent weeks to as little as two points, ahead of the National Coalition and Finns Party which are battling it out for second place. The results from these votes are often skewed due to differences in voter behaviour in different regions.
Officials said some 300,000 advance votes remained uncounted when polls closed at 1700GMT.
"He said" 'That's a big question for me.
"For example the cuts the government has made to education have been very much criticised because education is something that we in Finland very much treasure". The Finns Party used the debate as a wedge issue to attract voters skeptical of the costs of further action.
At one of its rallies on the eve of the vote in Myyrmaki, a disadvantaged suburb of the capital, a crowd of people, young and old, clamoured around party leader Jussi Halla-aho, asking for autographs and congratulating him on the campaign.
The growing Finns Party ratings, on the other hand, appear to be driven by new supporters who have not voted in the past.
Other proposals include increasing the number of electric vehicles on Finland's roads and reducing meat consumption through taxes or serving more vegetarian food as part of publicly funded meals in places like schools and the military.
Voter Sofia Frantsi, 27, an architect from Helsinki, told The Associated Press "for everybody, it's about the climate".
Voters were choosing between 2,500 candidates from 19 political parties and movements for the Eduskunta legislature's 200 seats.
Tackling climate change and reforming Finland's social and health care system were key topics in the vote where established parties lost support to populists in line with an overall European trend.
The center-left Social Democratic Party tops a recent poll with 19% support.