AIB and Bank of Ireland warned the Government that the price banks could have to pay to use the State's guarantee may be so big that it would run the risk of 'destabilising the entire bank system'.
In a letter to the secretary general of the Department of Finance, David Doyle, from AIB CEO Eugene Sheehy and Bank of Ireland CEO Brian Goggin, the pair said: 'An unreasonably high premium would threaten the viability of even the strongest institutions.'
The letter, stamped 'Secret', was sent on October 1 2008, one day after the Government announced the bank guarantee.
In the letter, Mr Goggin and Mr Sheehy said there should be differentiation between different categories of banks, depending on how they were rated by markets. They also said there should be differentiation between banks, depending on how much support they give to the mortgage market.
The letter has been released to RTE News and Current Affairs under the Freedom of Information Act.
Bradford & Bingley was 'difficulty' for Ireland
The documentation also contains points for discussion for Taoiseach Brian Cowen for a meeting with President Sarkozy of France after the bank guarantee was announced.
The notes say: 'Lehmans messed up the world markets but Bradford and Bingley created real difficulty for Ireland given that some Irish institutions have similar, though better quality, UK assets.'
The notes say the 'greatest ever decline' in the Irish Stock Exchange indicated that the collapse could easily threaten the whole economic future.
The notes say that it would be 'helpful' if the European Central Bank made longer term funds available for banks.
The documentation also contains an e-mail from a Department of Finance official raising concerns about increasing the deposit guarantee for ordinary bank customers up to €100,000. The e-mail was written a day before the Government increased the guarantee from €20,000 to €100,000 on September 20 2008.
The official point outs that trebling the guarantee to €60,000 would be broadly in line which changes which Britain was making to its guarantee. But he adds: 'Anything over that - certainly to €100,000 - looks very hasty.'