Lewes District Council is one of the local authorities concerned they may lose millions of pounds held in Iceland banks.
East Sussex County Council and Wealden District Council told the Express they did not have money tied up in the country.
But Lewes District Council has a 1million deposit.
A spokesman said: 'Lewes District Council is one of many councils and public bodies with an investment in the Landsbanki Island UK bank. It has supported the move by the Local Government Association for urgent discussions with the Government.
'The council places deposits taking account of Fitch and Moody credited rated institutions and has a 1m term deposit yet to mature.'
Leader of Lewes District Council, Cllr Ann De Vecchi said: 'I agree with the Local Government Association comment that it does not expect "significant financial problems" in the short term as councils put money in a wide range of institutions and vital frontline services should not be affected, and that is the position at Lewes.
'The current position remains fluid and may well change. The way we use investment interest and structure the council's finances means we can deal with this situation without it affecting council tax levels. We firmly believe the situation is a consequence of the current global market instability and that the Government should assist the many councils affected. At the end of the day bringing stability to the world's financial institutions is essential for everyone and we believe that any support should come from the Government.'
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Weather for Lewes
Sunday 26 May 2013
Temperature: 6 C to 16 C
Wind Speed: 17 mph
Wind direction: West
Temperature: 9 C to 14 C
Wind Speed: 18 mph
Wind direction: South west