Mr Murphy said councils invested cash in good faith
The Scottish secretary has said he is "satisfied" with the outcome of talks aimed at recovering Scots council cash locked in Icelandic banks.
Jim Murphy travelled to Reykjavik for high-level talks with Icelandic Prime Minister Geir Haarde on agreeing a way forward.
Eight Scottish councils had a total of £46m in Icelandic banks before they fell victim to the global money crisis.
Strathclyde Fire Board and several charities have also had money frozen.
A Scottish Government source welcomed the Scottish secretary's move.
Mr Murphy said Scottish councils and charities had invested millions in Icelandic banks in good faith, before the country's banking system was severely hit by the global financial crisis.
Speaking after the meeting, he said: "This has been a positive visit. Mr Haarde and his government have been hospitable and helpful and we are all agreed that it is important to find a constructive and co-operative way forward that allows the technical experts to work on the detail of recovering UK savers' money.
"Our ultimate aim is a shared one, which is to achieve the stability of the banking sector, not only here in Iceland but across Europe and further afield.
"The UK Government's primary objective remains to secure the investments of the 300,000 depositors, plus many local authorities, held in the failed Icelandic banks.
"This includes as many as 30,000 Scottish domestic savers and a significant number of Scottish local authorities. So there is lots of technical work to be done but I am determined that progress is made."
Total UK deposits are estimated at about £4bn in Iceland's financial institutions.