The Tánaiste and Minister for Finance, Brian Cowen, has said the pledge by the British Chancellor of the Exchequer to guarantee all existing deposits at Northern Rock includes the bank's customers in Ireland.
There were queues outside its branches in the UK for the second day running.
The queue outside Northern Rock's headquarters on Harcourt Street in Dublin was greatly reduced today.
Northern Rock staff at the bank's branch at Harcourt Street this afternoon handed over cheques to a small number of customers gathered outside the bank.
This was after customers were given a slip of paper requesting them to return at 4pm when they would receive their savings.
Financial authorities in both Ireland and Britain are waiting to see if the run on the bank's cash will subside today.
This is after the Bank of England on Friday stepped in with emergency lending for Northern Rock.
The bank lends a large amount for mortgages, and finances this with mostly money lent from other banks.
However, money markets stopped lending money due to the crisis in the US sub-prime mortgage market.
Speaking on RTÉ's Morning Ireland, senior manager with Northern Rock Brian Kavanagh, said Northern Rock's funds were guaranteed and there was plenty of cash to cover all customer transactions.
More than £2 billion has been withdrawn by customers since the bank applied for emergency funding from the Bank of England last week.
However, the embattled bank made a recovery on the FTSE 100 in London this morning, pulling back 10% to 312 pence this afternoon.
Last night's intervention by the British Chancellor of the Exchequer, Alistair Darling, was aimed at trying to discourage customers from withdrawing their money from Northern Rock, and threatening the bank's future.
The guarantee that all deposits at the bank would be covered goes beyond the existing British Government guarantee scheme that protects 90% of deposits up to €35,000.
This morning, Northern Rock has placed an advertisement in all Irish newspapers to apologise to its customers, and say that it is open for business as usual.
It says it remains a well-managed company and continues to be a safe place for people's savings.
But whether these latest re-assurances allay the fears of customers and investors remains to be seen.
Alliance and Leicester, Britain's eighth largest lender, saw its shares drop by 31% yesterday as speculation grew that it may be in similar trouble to Northern Rock.
But, like Northern Rock, Alliance and Leicester stock recovered this afternoon and had won back 32% to 795 pence this evening.
