LGA Chairwoman Margaret Eaton says there will be no threat to frontline services
Financial experts have been sent into three councils which could face short-term problems owing to their share of £858.3m in troubled Icelandic banks.
Two district councils - Uttlesford in Essex and Wyre Forest in Worcestershire - have been named as two of the three.
Ten more are in touch with the government's special "rapid response unit", to help them "assess their position," minister John Healey said.
There was "no reason" to think services or wages are at risk, he said.
The government has set up a "rapid response unit" to deploy finance experts from other local authorities to councils facing "severe short-term difficulties".
'No immediate concern'
Uttlesford confirmed it had £2.2m deposited in Landsbanki - one of the Iceland banks taken into receivership - which amounted to a fifth of its annual budget. A spokesman said he was confident that services would not be affected.
Wyre Forest Council, based in Kidderminster, had £9m deposited in three Icelandic banks but also said there was no immediate concern over services.
Why are these councils investing taxpayers money in an Icelandic bank?
Daniel Kawczynski Conservative MP
Council leader John Campion said they had not been visited from the team on Wednesday but had been told it would be one of the first three to get one.
He added: "The council is always receptive to any advice which will help in recovering the £9m investment in the banks affected."
Plymouth City Council, which has £13m invested in three Icelandic banks, has said it faces a £9m shortfall in October.
But it says it has some investments maturing in November which could be used to repay any borrowing. It has not needed help from the finance teams, a spokeswoman said.
The government met members of the Local Government Association to discuss the issue earlier - 116 authorities, including councils and police authorities in England and Wales, and fire authorities in England had invested money in Icelandic banks.
In a joint statement, the LGA and ministers said there had been "positive joint working" and the government "continues to work with the Icelandic authorities to ensure a fair deal for all UK depositors".
Several Icelandic banks have failed and will not release deposits
In the Commons earlier, local government minister John Healey had been urged to name the councils which had been contacted.
Shadow local government minister Eric Pickles told him: "I think a number of people who don't understand the nature of local government finance are going to become unduly concerned and worried about cuts in services and reliability. I think it would be better for it to be out in the open."
For the Lib Dems, Julia Goldsworthy added: "I think people will be very concerned that initially we were told that no council had done anything reckless and no-one would suffer short-term problems and now we are being told that some people might."
The government has not offered to guarantee the councils' deposits as it has done for individual British savers.
But Mr Healey told MPs that councils which found themselves in trouble would not be "left without support".
"That's why for the 13 that have reported they may face short-term difficulties, we are stepping in immediately."
Conservative MP Daniel Kawczynski asked: "Why are these councils investing taxpayers money in an Icelandic bank?"
He said his own local councils had not despite being "under the same pressures to maximise return on investments" and suggested councils were not getting enough money from the government.
Mr Healey said it was not true councils had been under pressure to "maximise investments" and had simply been "required to make investments prudently" and to prioritise "security and liquidity".
The BBC understands a third of the £858.3m invested could be recovered from two of the banks whose UK assets were frozen last week.
Speaking after the meeting with ministers, LGA chairwoman Margaret Eaton said: "As far as the administrators in this country are concerned, we've been working closely with them and we're more optimistic than we were this time last week. "
It will be mid-November before administrators Ernst & Young can estimate accurately how much money can be recovered from the collapsed UK operations of the Heritable and Kaupthing banks.
The likelihood of getting back the other two thirds of the money, held directly in Icelandic-based institutions, is less certain.
The UK Treasury has said it is working with the Icelandic government to ensure all depositors get their money back as soon as possible.
It has offered Landsbanki - one of banks nationalised by the Icelandic government - a £100m loan to help it repay some of its UK creditors.
Iceland's attractive interest rates had lured many customers from overseas, but last week its biggest banks had to be nationalised.
The LGA is demanding an inquiry into why credit rating agencies continued to rate Icelandic banks relatively highly just days before they collapsed.
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