The two parties have been running Iceland since January, when protests over an economic collapse forced the previous center-right government to step down.
The Social Democrats of PMJohanna Sigurdardottir wants to apply quickly for European Union membership, a plan that is opposed by the Left-Greens. "This is the only option we have to safeguard economic stability in the country," Sigurdardottir told state radio.
Iceland's currency and financial system crashed at the end of 2008 when the island's banks were no longer able to pay their huge debts, built up through years of overseas expansion. The banks were taken over by the government, which had to agree to painful reforms under a $10-billion, IMF-led bailout plan.
On a debate program late on Sunday, Sigurdardottir indicated the EU negotiations were going to be difficult as it was "the hardest thing we have to find a solution to" in the talks. Left-Green leader Steingrimur Sigfusson said the EU issue was a "large, unbridged difference" for the parties. The tone of the remarks contrasted with comments before the election, when the leaders said they were confident they could find a compromise on taking the EU question forward.