"Banking reforms do not come bigger than those proposed by President Obama," the BBC's business editor Robert Peston said.
This may mean that some of the US' biggest banks, such as Bank of America and JP Morgan, whose shares were badly hit, may have to be broken up.
The industry lobby group for banks suggested Mr Obama was trying to return the US to the past.
"The better answer is to modernise the regulatory framework and not take the industry and the economy back to the 1930s," said the Financial Services Roundtable, an industry group that represents large Wall Street institutions.
In the UK, shadow chancellor George Osborne said that if the Conservatives won the next general election, they would impose an identical dismantling of UK banks to those suggested by the US president.
City Minister Lord Myners said the US proposals were "very much in accordance with the direction we have been setting".
Mr Obama's move is his first proposal since Republican Scott Brown's shock victory in Massachusetts to win a Senate seat.
The Republican victory may make it harder to get Mr Obama's proposals passed in the Senate, as they are more likely to get held up in political wrangling.
"This is a political effort because of what happened in Massachusetts," said economist Peter Morici of the University of Maryland.
The US President believes that banks are back to their bad old ways too soon after their woes led to the biggest bank global bail out in history
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