The Swedish central bank said it believed that Kaupthing was solvent, but was suffering temporary liquidity problems that could have wider repercussions.
"To safeguard financial stability in Sweden and ensure the smooth functioning of the financial markets, the Riksbank has therefore decided to grant liquidity assistance to Kaupthing Sverige,'' it said in a statement.
In Britain, Alistair Darling, the treasury chief, said deposits of British savers with Icesave, the online arm of Landsbanki, the bank nationalised by the Icelandic government, would be guaranteed.
Icesave had stopped customers, including thousands in Britain, from withdrawing money from their accounts and British regulators have said it is likely to file for bankruptcy.
Bolstering the British support, savings bank ING Direct UK said it is buying more than $5.3bn of deposits held by around 180,000 British savers with two other Icelandic-owned banks, Kaupthing Edge and Heritable Bank, which is owned by Landsbanki.
The intervention of the British and Swedish authorities underscores the effect that a full-blown collapse of Iceland's financial system would have on the rest of Europe, given the heavy investment by Icelandic banks and companies across the continent.
One of Iceland's biggest companies, retailing investment group Baugur, owns or has stakes in dozens of major European retailers, including enough to make it the largest private company in Britain, where it owns a handful of stores such as the famous toy store Hamley's.
Kaupthing has also invested in European retail groups, and created debts of more than $5.25bn by Kaupthing in five years to help fund British deals.
The Icelandic government said on Tuesday that it had extended its own $680m loan to Kaupthing to tide it over.
The government is also due to send a delegation to Moscow this week to negotiate the terms of a loan that it hopes with bolster its depleted foreign exchange reserves.
After watching the currency free fall for several days, the Central Bank of Iceland said on Tuesday it would fix the exchange rate of the krona at 175, a level equal to 131 krona against the euro.
The speed of Iceland's downfall in the week since it announced it was nationalising Glitnir bank, the country's third largest, caught many by surprise, despite warnings it was the "canary in the coal mine'' of the global credit squeeze.
With the deregulation of its financial market in the mid-1990s and subsequent stock market boom, Iceland had transformed itself from the poor cousin in Europe to one of the region's wealthiest countries.