Geir Haarde says he is sending people to Moscow to hold talks over a loan
Customers of the Icesave internet bank have been warned they will probably have to claim compensation for money held in their savings accounts.
The authorities in the UK are preparing for the bank's parent in Iceland, Landsbanki, to be declared insolvent.
The Icelandic government took control of the country's second-biggest bank on Tuesday to keep it afloat.
Icesave is not currently allowing customers to take money out of their accounts or to put in deposits.
Claims from Icesave's UK customers will be handled by the Financial Services Compensation Scheme (FSCS).
Halldor J Kristjansson, the new manager of Landsbanki, said it had not helped that customers in Britain wanted to take out a large chunk of money after the news broke about the nationalisation of Glitnir, the third-largest Icelandic bank, last week.
"There is always a certain danger that there will be large withdrawal of savings and that by itself created additional problems on top of everything else, there are so many interwoven factors but that wasn't the main problem although it is very big," he said.
Under the depositor protection arrangements in Iceland and the UK, the Icelandic authorities will be liable for the first 20,887 euros (£16,300) of compensation.
We are gearing up to be ready to do whatever we can in order to get compensation back to UK savers as quickly as possible
Icesave has 350,000 savers in the UK and Netherlands, with about £4.5bn of deposits.
The decision to freeze accounts dismayed customer Mike Davis, 62, who has £75,000 in retirement savings locked up in an Icesave account until 25 October.
His daughter also has savings there and his partner, Pam Henson, 67, has £23,000 with the same bank.
The couple are getting married on 1 November, and Mr Davis, who lives in Gloucestershire, said he was "shaking with worry" when he heard about problems with Icesave.
"This cannot have come at a worse time. It is a pretty devastating blow," said Mr Davis, a landscape architect.
"I haven't slept for a couple of days. This was money put away for retirement."
He was expecting a long process of trying to recover savings and called for governments to guarantee 100% of savings.
Landsbanki is the second Icelandic bank to be taken over to prevent a collapse of the country's banking system.
What we are doing here is saving a banking system
Geir Haarde, Iceland's prime minister
In an announcement on state radio, Commerce and Banking Minister Bjorgvin Sigurdsson said the board of directors of Landsbanki had been dismissed and the bank put into receivership.
He said the state takeover was made "in co-operation" with Landsbanki and the bank would stay open and operate as normal.
Glitnir, the country's third-largest bank, was nationalised last week to stop it being driven into bankruptcy by the international financial crisis.
In a parallel move, Iceland's largest bank Kaupthing has been given a loan of 500m euros from the country's central bank.
"The central bank of Iceland has provided Kaupthing with a 500m euro loan to facilitate operations, and Kaupthing is committed to working with the government to ensure regular workings of the Icelandic financial system," the bank said in a statement.
On Monday, the Icelandic government passed emergency legislation to try to rescue the country's banking system and avoid what Prime Minister Geir Haarde described as "national bankruptcy".
Icesave announces it is freezing its customer's accounts
This included an unlimited guarantee for all bank customers' savings accounts.
"What we are doing here is saving a banking system - saving the domestic banking system - and making sure that it can function properly," he said after the decision to rescue Landsbanki.
Meanwhile, the Icelandic government has asked Russia to give it a loan of 4bn euros lasting for three to four years, to strengthen its foreign exchange reserves.
"We have not received the kind of support that we were requesting from our friends. So in a situation like that, one has to look for new friends," Mr Haarde said.
The website of Icesave tells customers: "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," it adds.
A spokeswoman for the bank said the website was not operating "due to technical difficulties", but did not offer any further reason for it being down.
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