The polling stations in Saturday's election closed at midnight Swedish time and when just over 30 percent of the votes were counted, the three ruling parties have 38 of the Althingi's 63 seats, Morgunblaðið reported.
The coalition has ruled for the past four years.
In addition to the Green Left, it consists of the national conservative Independence Party and the liberal Progress Party.
The winner of the election so far is the Progress Party, which climbs almost six percentage points and right now has squeezed five new seats in the Althing.
On the other hand, both the Green Left and the Independence Party seem to be backing between one to two percentage points each.
A record number of parties are in the fight for seats in the Althingi and as many as nine of them have a chance to reach the five percent barrier and tighten seats, which could open up new coalitions.
The final election result is not expected until later on Sunday.