* Prime Minister meets centre-left ally after election win
* PM says disagreement over EU won't be obstacle * Centre-left in historic win of majority
* Centre-right blamed for crisis after collapse of banks
(Adds PM quotes after meeting)
By Patrick Lannin
REYKJAVIK, April 26 (Reuters) - Iceland's Social Democrats began negotiating over a centre-left government coalition on Sunday with plans to push for European Union membership talks for the crisis-hit nation.
Caretaker Prime Minister Johanna Sigurdardottir, 66, claimed victory in an election on Saturday held three months after protests over an economic meltdown forced a conservative-led government out of office.
Sigurdardottir, who wants to start negotiations quickly on EU membership and then have a referendun, held a first round of talks with caretaker coalition ally the Left-Green party.
The Left-Greens have been opposed to EU entry but Sigurdardottir and the Left-Green leader have said they think they can find a compromise to take the EU question forward.
On Monday she was due to meet the president, who gives the formal authority to form a government.
"The talks today were productive and friendly," she said on the RUV state broadcaster after meeting Left-Green leader Steingrimur Sigfusson.
She earlier told the Morgunbladid daily that she did not expect the coalition talks to founder on the EU issue.
The parties must also find budget cuts and revenue rises, possibly via tax increases, to get state finances back into order and reduce a huge budget gap caused by meltdown.
They must also deal with surging unemployment.
She has said the election result for her party and the fact that pro-EU parties have won a majority in parliament showed voters backed her stance on seeking EU entry.
The Social Democrat and Left-Green caretaker government, which came in after the old administration fell, won 34 seats for a slim 3-seat majority in the 63-seat parliament.
The Social Democrats won 20 seats and the Left Greens 14.
Birgir Gudmundsson, professor of politics at the University of Akureyri, said a bill for EU membership talks could be presented to parliament, allowing the Left-Greens to abstain and the Social Democrats and pro-EU parties to push it through.
Even if parties agree on membership talks, a referendum win is not a foregone conclusion as opinion polls show Icelanders remain split on EU entry.
Sigurdardottir has said she can convince them of the benefits. She also wants to adopt the euro within four years.
The election showed the depth of anger at the long-ruling Independence Party, which oversaw Iceland's boom years but was blamed for the economic crisis that erupted last year when banks collapsed under a weight of vast debts.
It had its worst election and fell to 16 seats from 25 at the last election in 2007.
Icelanders took to the streets in January after their banks buckled under debt that was used to fuel aggressive overseas expansion into financial services.
The economy went into meltdown and the currency plummeted, forcing the government to agree a $10 billion IMF-led rescue for the nation of 300,000.
Iceland still expects the economy to contract by more than 10 percent this year and inflation was 15.2 percent in March. (Additional reporting by Omar Valdirmarsson; Editing by Angus MacSwan)