The announcement comes after RBS chief executive Stephen Hester turned down a £1m bonus after public outcry over the payment.
The government said today that it would not “micromanage” RBS and that remuneration for members of staff was an issue for the taxpayer-owned bank itself, the BBC reports.
It refused to block bonus payments to other top RBS bankers as proposed by Labour leader Ed Miliband.
A government spokesperson said: “The prime minister’s view was that he wanted the bonuses to be lower.
“He always made it clear that it was a matter for Mr Hester whether he took that bonus or not, and that should remain the case.
“Reward for good performance is not in itself a bad thing.”
Chancellor George Osborne welcomed Hester’s move to give up his bonus as a “sensible” decision.