The government says it will increase the levy on bank profits to £2.5bn this year - raising an extra £800m.
Chancellor George Osborne said he was able to increase the levy because banks' performances have been stronger than expected.
The levy, he told Today presenter John Humphrys, ensured that the banks were making a "fair contribution" to society.
He said he wanted the banks to be aware of the tax so he could enter into negotiations with them over bonuses and lending in "good faith".
What the government wanted from the banks was "more lending, more tax, a bigger contribution to society and less bonuses than they paid last year" he said.
"I'm not prepared to conclude a deal [with the banks] until I think it's a good one".
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