Landsbanki was one of the banks that was taken over by the authorities
Charities in the UK that lost millions of pounds when the Icelandic banking system collapsed should get a bail-out, according to a committee of MPs.
But local authorities that suffered the same fate should not be compensated, the Treasury Select Committee said.
Deposits held by British citizens living outside the UK with savings in these banks' offshore arms should also not be covered.
Iceland's financial sector collapsed last October, riddled with bad debt.
The committee's report into the Icelandic fall-out is the first of a series of findings on the banking crisis.
The committee recommended a one-off compensation package for charities which lost an estimated £120m of deposits with the Icelandic banks.
Many of these charities were too big to be covered by the government's deposit insurance scheme and face trying to get back funds from the banks' administrators.
"At a time when more people than ever may be faced with difficult circumstances, we believe that it is imperative that charities have access to the funds that were provided to them by the public," the report said.
It also called for a fresh look at the classification of charities under the government's protection scheme to avoid similar cases in the future.
The committee did not offer the same support to local authorities that had sunk a total of nearly £1bn into accounts with the Icelandic banks.
The report acknowledged that, although some councils would "feel hard done by" regarding the limitations of government support for them, it would be "perverse" for them to be compensated.
"They have a duty to the taxpayer diligently to protect the money they are investing on their behalf. Some authorities have shown themselves to be better than others in this regard," the report said.
"Under these circumstances, it would seem perverse to reward those authorities who failed to protect their investment with yet more money from the taxpayer."
Unsurprisingly, the conclusions were welcomed by a charities' group, but criticised by the Local Government Association (LGA).
"We now need the chancellor to act swiftly and compensate those [charities] which have lost funds," said John Low, chief executive of the Charities Aid Foundation.
Margaret Eaton, chairman of the LGA, said: "There must be a consistent and fair approach to compensation. If charities are to be compensated, why should there no relief whatsoever for the council taxpayer? Councils provide vital services to society's most vulnerable people."
Iceland was thrown into economic chaos when its three biggest banks were taken over by the authorities.
Iceland suffered more than most countries from the downturn
First to lose independence was First Glitnir, closely followed by Landsbanki, which owns Icesave - an internet bank used by many UK customers.
Finally, Iceland's biggest bank, Kaupthing, was nationalised in October. Iceland's government blamed UK Chancellor Alistair Darling for undermining confidence in Kaupthing by using anti-terrorism laws to seize Landsbanki's UK assets.
Mr Darling said that UK depositors and creditors were unlikely to be protected to the same extent as Icelandic ones.
"We also have seen no evidence that Kaupthing would have survived if the Chancellor had not expressed his views," the report concluded.
However, it expressed concern over the Financial Services Authority's "impotence" to tackle the fears raised by the former boss of Singer and Friedlander about the takeover by Kaupthing in 2005.
Hundreds of letters were sent to the committee from British savers who had deposits with Landsbanki's Guernsey arm and Kaupthing Singer and Friedlander's Isle of Man operation.
But the committee recommended that the UK government could not compensate losses by British citizens in jurisdictions outside the direct control of the UK.
Some 2,000 Landsbanki depositors in Guernsey have received 30p in the pound on an estimated £117m. Around 10,000 savers with £840m tied up in Kaupthing's Isle of Man business have received £105m back so far, but they do not know how much they will receive in total.
In 2008, Kaupthing Singer and Friedlander (Isle of Man) took over the Isle of Man subsidiary of the Derbyshire Building Society. Those with long-term bonds had no chance to remove their funds without a penalty.
Offshore savers using independent financial advisers were not advised of the changing risk profile of their savings, the committee found.
"This aspect of our banking crisis inquiry has also raised many new questions about issues such as consumer advice and cross-border regulation of financial institutions," said the committee's chairman, John McFall.