* Prime Minister's alliance set for outright majority
* PM wants quick talks to enter EU * Economic crisis triggered by collapse of banks
By Patrick Lannin
REYKJAVIK, April 26 (Reuters) - Social Democrat Prime Minister Johanna Sigurdardottir claimed victory in Iceland's election on Sunday after street protests over an economic meltdown toppled the previous conservative-led government.
With 42 percent of votes counted, a state TV projection showed her Social Democrat/Left-Green caretaker government that stepped in after the old administration fell would win 35 seats, a majority of four in the 63-seat parliament.
"I believe this will be our big victory," the 66-year-old Sigurdardottir, leader of the Social Democratic Alliance, told cheering supporters.
The results from Saturday's election were set to put the pro-European Union Social Democrats in the driving seat of the centre-left coalition, though it must find a compromise with the anti-EU Left-Greens on starting entry talks with the bloc.
Sigurdardottir, who is convinced she can find such a compromise, has said Iceland should quickly start talks and then eventually hold a referendum on EU entry.
Voters punished the centre-right Independence Party, which led the previous coalition government that surrendered power in January over blame for last year's crisis in which the economy imploded as banks collapsed under a weight of vast debts.
The television projection gave the Independence Party 15 seats, down from 25 at the last election in 2007.
TOUGH DECISIONS
Though heading for an outright parliamentary majority, the new government faces tough decisions to cut spending, raise revenues and find ways to reduce surging unemployment.
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 Iceland's 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.
On the issue of EU entry, opinion polls show Icelanders remain split but Sigurdardottir has said that once they have understood the benefits they would back such a move.
If Iceland entered the EU within a year to 18 months, it would be able to adopt the euro within four years, she says.
"I really hope that the parties on the left will stand up as winners because I think they are more capable of leading us out of the crisis," said teacher Hrafnhildur Asthorsdottir.
A new party, formed from the grassroots movement that led the street protests, was set to win four seats, the television projection showed. (Additional reporting by Omar Valdirmarsson; Editing by Ralph Gowling)