Kaupthing Edge was the UK arm of Kaupthing
A backlog of payments causing concern for former customers of Kaupthing Edge in the UK should be cleared by Friday.
The accounts of savers with Kaupthing Edge, part of Iceland's biggest bank - that was nationalised last week, have been transferred to ING Direct.
ING said that it was honouring all payments made during the upheaval and no interest would be lost by customers.
It said it could now give a "firm assurance" that delayed payments would arrive by the end of Friday.
"It has taken us longer to resolve the issues at Kaupthing Edge than we expected due to the significant disruption caused when the business was taken into administration," a statement for ING Direct said.
"Understandably, customers have been asking for clarification on when this issue was going to be resolved, but this is the first time we have been in the position to give firm assurances."
ING Direct agreed to take over the £2.5bn of deposits of 160,000 UK customers of Kaupthing Edge on 8 October.
But during the handover, customers complained of delays in the completion of transactions and some feared their money had been lost.
Meanwhile, around 3,000 UK customers who did not have internet accounts with the Kaupthing are having to claim compensation for lost savings from the Financial Services Compensation Scheme.
Application forms are being sent to them this week.
Another Icelandic bank - Landsbanki - closed on 7 October. This had 300,000 customers in the UK who had accounts with the Icesave brand.
These customers have been unable to make withdrawals or deposits since, and will also have to claim compensation for lost savings.
A spokesman for the FSCS said dialogue between the UK and Icelandic authorities was ongoing and it hoped more information would be available to savers by the end of the week.