But the Grimsson has yet to sign it into law and 23 per cent of the island nation's electorate - 56,089 people - have signed the petition, organisers said.
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.
InDefence, the group responsible for gathering the signatures, said the Icesave legislation represented a "huge risk" for Iceland's economic future.
"All projections based on realistic assumptions ... showed without doubt that Iceland would be unable to meet the payments stipulated by the Icesave loan agreements as set out in the disputed legislation," a statement from the group said.
But repaying the money could also hold some benefit for Iceland as the longstanding dispute has held up payment of some aid funds from international lenders.
Morton Kraemer, a credit analyst with rating agency Standard & Poor's, said that while the bill "will add significantly to the general government's debt burden" the resulting aid payments would help Reykjavij relax financial controls put in place during the financial crisis.
"It [passage of the bill] is a decisive step to unlock further disbursements of up to 2.3 billion euros from the International Monetary Fund and from bilateral loans from Nordic governments," he said.
Passing the Icesave legislation would also boost Iceland's hopes of swift entry into the European Union, a move Iceland's population is only lukewarm about.
Icesave was an online subsidiary of Iceland's Landsbanki bank, which had to be rescued in October 2008 as the global credit crunch hit.