The payout has stirred up considerable resentment among many ordinary Icelanders hard hit by their country's financial meltdown in 2008.
Skarphedinsson told the paper the deadline of the referendum meant "we're under high pressure like never before. Those are good conditions for achieving an agreement."
Skarphedinsson said that if Saturday's referendum went ahead a "No" vote was certain and that the negotiations would be further drawn out.
The Icesave deal is deeply unpopular with the Icelandic population and there is widespread feeling that taxpayers are being left to foot the bill for mistakes made by financial firms operating under the watch of other national regulators.
Rejection of the Icesave bill would likely freeze the foreign aid needed to resuscitate Iceland's economy and cloud its prospects of joining the European Union (EU).
Support for accession has been falling in past months and membership now opposed by more than half of Icelanders, nearly twice the level seen just after the 2008 financial crisis in which three of Iceland's leading banks collapsed.
"Attitudes towards EU membership are changing drastically," Gudbjorg Andrea Jonsdottir, a research director at pollster Capacent, said.
"There is a lot of anger over the Icesave saga and, rightly or wrongly, some blame is directed at the EU, which only adds to long-held Icelandic suspicions about Brussels."
Skarphedinsson was hopeful Icelanders would accept any cancellation of the referendum should a new deal more favourable to Iceland be struck.
|The payment of the $5.7bn, is equivalent to nearly 40 per cent of the country's GDP [AFP]
But the ballot may be difficult to cancel without support from opposition parties, who are trying to turn the referendum into a vote on the centre-left government.
"If we reach a deal in the short-term, the conditions would be so good that there wouldn't be any great frustrations among the population," Skarphedinsson said.
Britain and the Netherlands have proposed softer terms than those agreed to late last year, but talks broke down last week as Iceland held out for a better deal.
Iceland, however, has little choice but to push for an agreement because Britain and the Netherlands want to settle the Icesave matter before funds from the International Monetary Fund (IMF) can resume and help rebuild its economy.
The measure foresees staggering through to 2024 the payment of the $5.7bn, which is equivalent to nearly 40 per cent of the country's annual gross domestic product.
Johanna Sigurdardottir, the prime minister, has tried to play down the expected rejection of the Icesave bill, which she pushed through parliament at a great political cost but which was rejected by the president, triggering the referendum on March 6.
Icesave was an online subsidiary of Iceland's Landsbanki bank, which had to be rescued in October 2008 as the global credit crunch hit.
It had attracted thousands of savers due to its high interest rates.