* Iceland election ends, early results show centre-left win
* Prime minister says vote is historic
* Prime minister wants quick talks to enter EU, adopt euro
(Adds polls close, first results, PM quotes)
By Patrick Lannin
REYKJAVIK, April 25 (Reuters) - Iceland's centre-left parties were heading for victory in an election on Saturday after protests over the country's economic meltdown toppled the previous conservative-led government.
A projection on state television RUV from initial results of the voting, which ended at 2200 GMT, showed the Social Democrat/Left-Green caretaker government that stepped in after the old administration fell would win 35-36 seats, a majority in the 63-seat parliament.
"There is good reason to smile. If this will be the result, it is a historic victory," said Prime Minister Johanna Sigurdardottir, the 66-year-old leader of the Social Democratic Alliance.
Voters looked to have punished the centre-right Independence Party, which led the previous coalition government. That administration collapsed in January, widely blamed for last year's crisis in which Iceland's economy imploded as its banks collapsed under the weight of vast debts.
The television projection gave the Independence Party 15 seats, down from 25 at the last election in 2007.
Though heading for a parliamentary majority, the new government faces tough decisions to cut spending, raise revenues and find ways to reduce surging unemployment.
EU QUESTION
The parties also have to find a compromise between their differing views on the European Union in order to start membership talks and later hold a referendum.
The Social Democrats are in favour of joining the EU, but the Left-Greens are opposed. Sigurdardottir has said she is confident she will be able to find a compromise with the Greens.
Polls show Icelanders remain split, but Sigurdardottir said that once they understood the benefits they would back EU entry.
If Iceland entered the EU within a year to 18 months, it would be able to adopt the euro within four years, she said.
Icelanders took to the streets in January after their banks buckled under a heap of debt that was used to fuel aggressive overseas expansion into financial services.
The economy went into meltdown and its currency plummeted, forcing the government to agree a $10 billion IMF-led rescue for this 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.
"I really hope that the parties to the left will stand up as winners because I think they are more capable of leading us out of the crisis," teacher Hrafnhildur Asthorsdottir said.
A new party, formed from the grassroots movement that led the protests, was to get four seats, the TV projection showed. (Additional reporting by Omar Valdirmarsson; Editing by Mark Trevelyan)