Opinion polls ahead of Saturday's election had indicated that the ruling coalition of the Left-Green Movement, the conservative Independence Party, and the centre-right Progressive Party - which has been in power for the last seven years - was likely to be unseated.
With almost 60 pe cent of votes counted, the Social Democratic Alliance - last in government between 2009 and 2013 - was leading with 21.5 per cent of votes.
The Independence Party, led by Prime Minister Bjarni Benediktsson, was in second place with more than 19 per cent of votes cast after benefiting from a late surge in support.
Iceland's Prime Minister Bjarni Benediktsson dissolved parliament in October and called an election. (AP PHOTO)
The centre-right Liberal Reform Party, which polls had previously suggested could come in second, was in third place with 16 per cent of votes cast.
Katrin Jakobsdottir of the Left-Green Movement resigned as prime minister in April to run for the presidency, a bid she lost.Â
Her replacement Benediktsson dissolved parliament in October and called an election following escalating coalition disagreements and public discontent over migration and energy and housing issues.
Iceland's population has surged by 20 per cent in the past decade, the most significant increase among OECD nations, fuelled by high immigration rates, further pressuring housing and health care.
While inflation and interest rates have recently started to decline, the cost-of-living crisis reignited the question of EU membership in election debates.
Frostadottir, a 36-year-old economist, who took over as Social Democratic Party leader two years ago, is a champion of the Nordic welfare model.
