All deposits held with struggling bank Northern Rock have been guaranteed by the government and Bank of England.
Chancellor Alistair Darling said he wanted to put the matter "beyond doubt" by guaranteeing all existing deposits "during the current instability in financial markets".
About £2 billion is reported to have been withdrawn from the bank since it emerged on Thursday that the company had requested emergency funds from the Bank of England.
Mr Darling repeated the government's belief, echoed by the Bank of England and the Financial Services Authority (FSA) watchdog, that Northern Rock remains solvent and is merely experiencing "short-term liquidity difficulties" caused by the current global credit squeeze.
"People can continue to take their money out of the Northern Rock bank but if they choose to leave their money in the Northern Rock bank it will be guaranteed safe and secure," he said at a press conference on Monday afternoon.
He added: "We will continue to work here and internationally to do everything we can to maintain a stable and strong economy."
The decision comes after Conservative leader David Cameron called on the government to make a statement about the current situation.
The opposition leader said there were "a number of questions that need to be answered" about events that have left thousands of people queuing in the streets to withdraw their money from the bank.
Mr Cameron said the queues of worried savers "serve to remind us just how fragile the stability of the economy can be" and that the government should make reassuring people about the safety of their deposits its priority.
Mr Darling later said he decided to guarantee the deposits "because of the importance I place on maintaining a stable banking system".
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