The Icelandic stock exchange has said that share trading will remain suspended until Tuesday because of continuing "unusual market conditions".
Trading was suspended last Thursday after days of market turmoil and the government's decision to nationalise Iceland's three major banks.
UK councils and other public bodies have about £1bn invested and it is not known if their deposits are safe.
Icelandic and UK authorities are trying to establish a single claims procedure.
Government talks
A Treasury delegation spent the weekend in talks with their Icelandic counterparts.
Private customers with Landsbanki's closed internet bank Icesave Nerves over Iceland stock market ...
UK councils seek Iceland cash pledge ...
Councils seeking Darling meeting ... are protected by the UK's Financial Services Compensation Scheme.
And arrangements have been agreed "in principle" for a quick payout to retail depositors in Icesave.
But the Icelandic government has not extended protection to the £1bn of taxpayers' money invested by councils, police forces, fire services and charities.
Insolvency fears
So far, more than 100 local authorities in England, Wales and Scotland have revealed they have deposits worth £842.5m in total.
Fears are growing that some local government workers may not be paid this month because councils have payroll tied up in the banks.
And at least 60 UK charities fear they may have lost up to £120m of funds invested in failed Icelandic banks.
The Christie NHS Foundation Trust, based in Withington, Manchester, has revealed it could lose £7.5m.
Representatives from the board of the cancer hospital met with the Financial Services Authority and its lawyers over the weekend.
Iceland is crippled with debt and giving UK depositors their funds may depend on the country securing emergency loans from other countries or the International Monetary Fund (IMF).
Its debt is an estimated about £50bn, which is five times the total annual income of the country.
(BBC)
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