Around 300,000 Britons are thought to hold around £4 billion of deposits in Landsbanki's Icesave business, which they cannot now access due to the firm's entering administration earlier this month.
Due to the way in which Icesave was registered in the UK, the Icelandic financial regulator is obliged to cover the first £16,000 of deposits in the event of the bank's collapse.
However, the near-meltdown in the Scandinavian nation's financial system has made these repayments problematic.
Gordon Brown labelled Iceland's apparent unwillingness to guarantee the savings as "unacceptable".
The UK government then guaranteed that Icesave savers will get their money back eventually - but is pressing the Icelandic regulator to provide the funds.
"This round of discussions has ended but talks are not over and will be continued in the very near future," a government spokesperson said.
Chris