Technical glitches have prevented UK customers from withdrawing funds from Icesave - the Internet arm of Iceland's Landsbanki.
UK newspaper The Times says although Icesave customers have been able to access their online accounts, systems problems have prevented them from transferring funds.
According to the report, a message on the Icesave Web site admitted that the bank had been experiencing "intermittent faults" over the last 12 hours that "randomly" affected different groups of customers. Icesave said its IT team had resolved the issue.
But The Times says it was contacted this morning by readers that had been able to to look at their accounts but had not been allowed to take money out.
Landsbanki launched its Icesave Web-only banking service in the UK in 2006. Meanwhile fellow Icelandic bank Kaupthing launched its Internet savings services - Kaupthing edge - in the UK earlier this year.
But the recent economic turmoil in Iceland - last week the country's government nationalised banking group Glitnir and requested financial help from the US and Scandinavian countries - has raised concerns about how safe deposits actually are in Icelandic banks.
Mark Sismey-Durrant, chief executive of Icesave in the UK told BBC Radio 4's Money Box programme that deposits in Icesave accounts were safe and customers "shouldn't be nervous about the state of the bank".
Savers frozen out as Icesave website collapses - The Times
Icelandic banks reassure savers - BBC
Following on from yesterday's story, Icesave has now suspended all deposits and withdrawals from online accounts after the Icelandic Financial Supervisory Authority (IFSA) stepped in to take control of Landsbanki.
Although Landsbanki's domestic branches, call centres, ATMs and Internet operations are open for business as usual, it is not clear how the move affects Icesave's UK customers.
A notice on the Icesave site says: "We are not currently processing any deposits or any withdrawal requests through our Icesave internet accounts. We apologise for any inconvenience this may cause our customers. We hope to provide you with more information shortly."
However savers are protected under compensation schemes in Iceland and the UK. The first EUR20,000 held in accounts is protected under the Icelandic government's scheme. The remainder up to £50,000 is covered by the UK's financial compensation scheme.