Magnus Arni Skulason, one of the organisers of the petition, compared the repayment to financing the country's health service.
"We were able to represent our arguments to the president, and also on the occasion we handed over a petition to ask the president to reject the current Icesave bill," he told the BBC.
"The interest rate on the Icesave agreement for Iceland is like running the National Health Service of Iceland for six months."
The Icelandic government had threatened to resign if the deal was rejected by MPs.
"Approving the bill is the better option and will avoid even more economic damage," Finance Minister Steingrimur Sigfusson said during the debate.
Icesave - the internet arm of Icelandic bank Landsbanki, which offered high interest rates - failed in October 2008.
An original agreement negotiated with the British and Dutch governments was approved in August.
But subsequent amendments negotiated by the prime minister were rejected in both countries, forcing a fresh vote.
Under the new deal the money - which represents 40% of the country's GDP - will be repaid gradually, staggered until 2024.
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