With 80% of ballots counted, the governing centre-left coalition is marginally ahead of its centre-right Alliance rivals, with around 40% each.
The nationalist Sweden Democrats (SD) have won about 18% of the vote, up from 12.9% in the previous election.
A protracted battle to form a working coalition now looks a certainty.
Sweden uses a system of proportional representation, under which each party is allocated a number of seats in each constituency that is broadly in line with its share of the vote.
Both of the main blocs have refused to govern with the SD, although its leader said he was prepared to talk with all other parties
"We will increase our seats in parliament and we will gain huge influence over what happens in Sweden during the coming weeks, months and years," Jimmie Akesson told a party rally.