Politicians in the UK were quick to sign up to Mr Obama's proposals.
The Treasury said it would consider the US bank reform plans "very carefully," while City Minister Lord Myners said the US proposals were "very much in accordance with the direction we have been setting".
The government has recently focused mainly on tackling bankers' large bonuses - a source of public outcry - with a one-off "super-tax" and other measures.
Meanwhile, the Financial Services Bill is making its way through Parliament, aiming to give the Financial Services Authority more powers to regulate banking behaviour.
It would also force banks to hold more money in reserve, as well as creating a new Council for Financial Stability, which is intended to consist of Treasury, Bank of England and FSA officials.
But none of the planned legislation goes as far as what the US president has now proposed.
Shadow chancellor George Osborne said that the Conservatives would impose an identical dismantling of UK banks to what Mr Obama proposed if elected.
But he said he would want to see international agreement before implementing any change in the UK.
BBC business editor Robert Peston said Mr Osborne's comments would "generate profound fear in the boardrooms of Barclays and Royal Bank of Scotland".
"Banking reforms do not come bigger than those proposed by President Obama," he added.
Other nations also backed the proposals. "I think this is a very, very good step forward," said French Finance Minister Christine Lagarde.
Limiting risk taking
Mark Mardell, BBC North America editor
This looks like a sudden and fairly dramatic change of policy.
But the White House says it was agreed shortly before Christmas.
Getting new laws through the Senate won't be easy, but it will be a lot easier than pressing ahead with health care reform which now seems to have been put off to some indefinite time in the future.
For the Democrats, this plan has distinct advantages.
Some Republicans, like former presidential candidate John McCain, already support very similar ideas and may well back tougher new rules.
Those who don't can be portrayed as friends of Wall Street, acting against the interests of Main Street.
"While the financial system is far stronger today than it was one year ago, it is still operating under the exact same rules that led to its near collapse," Mr Obama said.
His proposals may mean that some of the biggest US banks have to be broken up.
What this means for foreign banks working in the US is still unclear.
They also include a ban on retail banks using their own money in investments - known as proprietary trading. Instead, banks would be limited to investing their customers' funds.
The moves follow popular anger at financial institutions, who have been paying large bonuses to staff even as they accepted government bail-outs to keep them going.
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