* Social Democrats, Left-Greens to form coalition 'in days'
* EU membership outstanding issue
STOCKHOLM, April 27 (Reuters) - Iceland's Social Democrats and Left-Greens, winners of a weekend election, are to agree within days on a coalition to rebuild the island following the financial crisis, the prime minister's spokesman said on Monday.
"We are looking at days," Kristjan Kristjansson, spokesman for Prime Minister Johanna Sigurdardottir, said when asked how long an agreement between the parties would take.
"They know the issues already, they have been working together, they just have to solve a few differences and they will find out very quickly if they can or cannot."
The two parties have been running Iceland since January, when public outcry over the financial crisis forced the previous government to step down.
They won a 3-seat majority in Saturday's vote and had informally agreed to extend a power-sharing agreement to work together to rebuild the island's shattered economy.
Kristjansson said there were a number of outstanding issues that the two parties needed to discuss, with possible entry into the European Union the biggest.
"If they are going to stay in government together ... they have to find a common ground some way or another," he said.
Sigurdardottir wants to start negotiations quickly on EU membership and then have a referendum. The Left-Greens have opposed EU entry, while the population is split.
Joining the EU is seen as a way to avoid a repetition of the economic meltdown Iceland suffered in the wake of the global financial crisis.
Iceland's economy is expected to contract more than 10 percent this year, sending unemployment soaring and bringing a painful end to years of growth which made the nation's population of 320,000 become among the richest in the world.
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 was forced to agree to painful reforms under a $10-billion, IMF-led bailout plan. (Editing by Janet Lawrence)