Mervyn King has called for "more boredom" in UK banking
UK Prime Minister Gordon Brown has warned action is needed to prevent the current financial malaise spreading.
Mr Brown said the first priority was "to stop the contagion to other countries, including in eastern Europe" where there were "problems emerging".
He added the IMF would have to create a new fund to help struggling nations.
It comes as the Bank of England said the world's financial firms had now lost £1.8 trillion ($2.8 trillion) as a result of the continuing credit crisis.
It also warned that 1.2 million homeowners in the UK now faced going into negative equity if house prices continued recent sharp falls.
The Bank gave the figures in its latest bi-annual Financial Stability Report.
UK Prime Minister Gordon Brown has called on China and oil-rich states to contribute to an IMF bail-out fund.
The idea is that the International Monetary Fund would be able to offer "substantially more" than the $250bn that it has at the moment to fund countries hit by the downturn.
"We must act now, we must set up the fund as quickly as possible," Mr Brown said, adding that he would discuss it with Chinese and Gulf leaders later in the week.
Warning that UK banks could now face stricter measures to avoid a repeat of the current credit crisis, the Bank said there may be "a need for a fundamental rethink of how to safeguard against systemic risk".
BBC Business Editor Robert Peston says global taxpayers have now spent £5 trillion to shore up the world's banks.
The UK recently announced it would be putting a total of up to £37bn into Royal Bank of Scotland, HBOS and Lloyds TSB.
The Bank of England's new estimate on global losses is double the estimate that it published in May.
Bank deputy governor Sir John Gieve said the "fundamental rethink" meant increasing capital and liquidity requirements at institutions.
According to the Financial Stability (FSR) report, the UK banking industry expanded over-rapidly when times were good, but lacked a solid foundation to cope when things turned bad.
Mr Gieve said: "Looking further ahead, we need a fundamental rethink of how to manage systemic risk internationally.
"We need to establish stronger restraints on the build-up of risks in the financial system over the cycle with the dangers they bring to the wider economy."
Measures mooted in the FSR include a "leverage ratio", which would peg back the growth in banks' balance sheets to the size of their capital.
Another suggestion is "dynamic provisioning", which would encourage banks to build up their reserves or take out insurance against having to seek funding injections.
The report points out that in 2001, UK customer lending was comparable to customer deposits.
But by the first half of 2008 the surplus of lending over deposits - "the customer funding gap" - was £700bn.
The report said banks should strengthen their finances by increasing customer deposits, holding more assets that are easy to sell and reducing reliance on wholesale money markets.
Last week Bank governor Mervyn King said the British banking system had been closer to collapse earlier this month than at any time since the start of World War I.
He also said that a "little more boredom" would be no bad thing for the industry.
The US Federal Reserve is to begin a two-day meeting on Tuesday to decide whether to reduce interest rates again.
The Fed is widely expected to cut rates to 1% from 1.5%, which would take rates to their lowest level since 2001.
Analysts expect that this move will lead to further cuts in interest rates in European banks.