* Centre-left caretaker government set to win Iceland vote
* Unemployment and state finances are key issues
* Government parties split on talks with EU, compromise seen
* Finance minister reassures IMF that programme on track
By Patrick Lannin
REYKJAVIK, April 24 (Reuters) - Iceland looks set for a historic swing to the left in an election on Saturday, three months after the long-standing conservative administration was brought down by the global economic crisis.
On the eve of the election, brought forward from 2011, the finance minister gave assurances that cooperation with the International Monetary Fund was on track and declared: "We are in no trouble."
Icelanders took to the streets in January after their banks collapsed under a heap of debt run up during the boom times and the government agreed a $10 billion IMF-led rescue.
Two opinion polls on Friday mirrored previous readings that the caretaker Social Democrat and Left-Green government will win the election and turn their minority coalition into a majority one likely to start entry talks with the European Union.
"That will be the first socialist majority in the history of Iceland," said Olafur Hardarson, professor in political science at the University of Iceland.
A poll for Morgunbladid daily and state broadcaster RUV showed the Social Democrat Alliance of Prime Minister Johanna Sigurdardottir, 66, set to keep the job, at 29.2 percent.
The Left-Green party, headed by Finance Minister Steingrimur Sigfusson, 53, was on 27.2 percent. He is also expected to retain that post after the election.
Voting starts at 0900 GMT on Saturday and ends at 2200 GMT.
First results are expected almost immediately after voting ends, though a final result is not due until early Sunday.
The centre-right Independence Party, which dominated governments since World War Two but fell into disgrace after the crisis, was heading for 23.6 percent, well down on the 36.6 percent from the 2007 election.
Going by the poll, the Social Democrats and Left-Greens would get 37 members in the Althing, five more than needed to form a majority. The Independence Party would have 15.
"The caretaker government has strong support in polls so we are relatively optimistic we will have a clear and good mandate from the Icelandic people by the end of Saturday," Sigfusson told Reuters Financial Television in an interview.
Sigurdardottir, a political veteran and popular former welfare minister, has turned her fire on the Independence Party.
"What is behind us now is neo-conservatism -- it was buried during the winter now behind us," she told a rally on Thursday.
SPLIT ON EU
Key issues for Icelanders are surging unemployment and worries about measures needed to sort out state finances.
The jobless rate hit 8.9 percent in March, sharply up from 1.9 percent in October, the month the full force of the crisis hit the island. The budget deficit is also expected to surge and the government is set to have to raise taxes and cut spending.
Sigfusson told Reuters that the IMF programme Iceland is following got delayed after the government change and that the country missed a tranche of its loan from the Fund in March. But he said the work was now back on track.
He added that talks with Nordic central banks, Poland and Russia were going similarly well. "We hope to have this more or less finalised in May or June," he said.
He said that if the coalition won the vote it would draw up plans for budget austerity measures by the middle of the year.
Another key issue is whether Iceland will start talks to join the EU, which it has so far avoided due to fear of losing sovereignty and control over its vital, large fishing stocks.
Polls show Icelanders remain split on whether to join, with a rise in support after the crisis having fallen.
The Social Democrats are strongly in favour of joining the EU, while the Left-Greens have been traditionally opposed.
However, the Left-Greens have said they are prepared to let the people decide so most commentators expect the new government to find a compromise by deciding to start EU entry talks and hold a referendum on the issue further down the line.
"Both parties are saying they will come to an agreement and I think they will," said Hardarson. (Reporting by Patrick Lannin; Editing by Charles Dick)