Shares in both banks fell sharply on Tuesday, with Royal Bank of Scotland losing 7% - the biggest decline on the UK's main FTSE 100 share index. Barclays lost 5.9%.
Under President Obama's proposals, retail banks would be banned from using their own money in risky financial transactions.
This would prevent them from investing in hedge and private equity funds, or engaging in so-called proprietary trading - investing their own money as opposed to that of their customers.
"This is a welcome move by President Obama that accords very much with our thinking," said Mr Osborne.
Vince Cable: "Now that Obama has done it in the States we've got to do it here"
"I have said consistently that we should look at separating retail banking from activities like large scale propriety trading - and that this was best done internationally."
Vince Cable, deputy leader of the Liberal Democrats called on the government to "get on with breaking up the banks".
"It is absolutely essential that Britain is not left behind by the US," he said.
"Britain is much more dependent on banks than America is and we are therefore much more vulnerable to banking crashes."
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