The British and Dutch governments voiced disappointment with the result of Saturday's referendum, in which almost 60 percent of voters opposed the repayment deal.
"We must do all we can to prevent political and economic chaos as a result of this outcome," Prime Minister Johanna Sigurdardottir told state television.
The issue will now be settled by the court of the EFTA Surveillance Authority (ESA), the European trade body overseeing Iceland's cooperation with the European Union.
"My estimate is that the process will take a year, a year and a half at least, Finance Minister Steingrimur Sigfusson told a news conference.
The debt was incurred when Britain and the Netherlands compensated their nationals who lost savings in online "Icesave" accounts owned by Landsbanki, one of three overextended Icelandic banks that collapsed in late 2008, triggering an economic meltdown in the country of 320,000 people.
Economists have said failure to resolve the issue means Iceland faces delays ending currency controls, boosting investment and returning to financial markets for funding.
But the center-left coalition government said it would not resign despite the defeat.
"The government will emphasize maintaining economic and financial stability in Iceland and continuing along the path of reconstruction which it began following the economic collapse of 2008," it said in a statement.
It said a fresh round of talks on further funding from the International Monetary Fund, which led a bailout for the island, would be delayed several weeks, but that it had enough foreign exchange reserves to cover debts maturing this year and next.
COURT CASE AHEAD
The proposed deal at issue in Saturday's vote set a clear timetable for repaying the Dutch and the British, including interest. But voters rejected the idea that taxpayers should foot the bill for what they see as bankers' irresponsibility.
"I know this will probably hurt us internationally, but it is worth taking a stance," Thorgerdun Asgeirsdottir, a 28-year-old barista, said after casting a "no" vote.
Dutch Finance Minister Jan Kees de Jager said: "This is not good for Iceland, nor for the Netherlands. The time for negotiations is over. Iceland remains obliged to repay. The issue is now for the courts to decide."
Economists have said the court route could be much costlier.
The government still hopes most of the debt will eventually be paid back from the estate of the bankrupt Landsbanki. Ratings agencies were following the vote closely. Moody's had said it might lower Iceland's rating in case of a 'no'.
Standard & Poor's analyst Eileen Zhang said a 'no' vote "might possibly result in a lengthy legal process and further uncertainties regarding the ultimate fiscal cost."
(Additional reporting by Sara Webb in Amsterdam and Avril Ormsby in London; Editing by Mark Trevelyan)
($1=113.31 Iceland Krona)