* Social Democrats, Left-Greens to form coalition 'in days'
* PM says talks on EU difficult but a priority
* Iceland president gives PM no deadline on coalition talks
(Adds PM meeting with president, details on committee)
By Patrick Lannin
REYKJAVIK, April 27 (Reuters) - Iceland's Social Democrats and Left-Greens, the winners of a weekend election, hope to form a coalition within days but agreement on whether to join the EU remains elusive.
On Monday, Prime Minister Johanna Sigurdardottir met President Olafur Grimsson who gave her as much time as she needed to conclude talks with the Left-Greens on a coalition.
Grimsson said on state radio the minority government, formed after an economic collapse forced the previous centre-right government to step down, now had a majority and would continue to run the nation as it has done since January.
"We are looking at days (for an agreement)," said Kristjan Kristjansson, spokesman for Sigurdardottir.
The main sticking point between the two parties, which held their first official talks on Monday, is whether to apply to join the European Union. EU membership is viewed by some as the best way to avoid a repetition of the island's meltdown which could result in the economy contracting 10 percent this year.
"They (the two parties) 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," said Kristjansson.
The Social Democrats of Sigurdardottir want to apply quickly for European Union membership, a plan which is opposed by the Left-Greens.
"This is the only option we have to safeguard economic stability in the country," Sigurdardottir told state radio.
Local media said the two parties have set up a working group to address questions about the EU, such as what kind of referendum would be held.
The Social Democrats and Left-Greens won a 3-seat majority in Saturday's vote for the 63-seat parliament.
STILL SPLIT
On a debate programme late on Sunday, Sigurdardottir indicated the EU negotiations were "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, difficult, unbridged difference" for the parties.
Opinion polls show the population is also split.
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. Unemployment is set to soar among the nation's population of 320,000, once among the richest in the world.
Kristjansson said there were a number of possibilities to solving the EU question.
"If they want to stay in government together they have to solve the issue, either by saying they will do nothing about it, or that they will call a referendum and simply ask the people what should be done, or that they will agree to form a committee to research the issue, or whatever," he said.
"They have to find a common ground, some way or another." (Additional reporting by Omar Valdimarsson; editing by Robert Woodward)