David Cameron is facing pressure to explain how RBS chief Stephen Hester was allowed to be awarded a £963,000 bonus after Ed Miliband and Boris Johnson attacked the "bewildering" payout.
Describing RBS as a "Soviet" style bank, the London mayor said it was "far-fetched" to think the bank's bonus system was not controlled by ministers and that the government should have acted to block the near £1m sum.
"I find it absolutely bewildering because RBS occupies the same status in the economy as Gosbank did in the Soviet Union: it's a state-owned bank," he told the BBC.
"This is not a free-booting, private sector, risk-taking enterprise, this is a state-owned concern that taxpayers have had to step in and bail out.
"The idea that this is not in the control of the government seems to me to be far-fetched. Stephen Hester is an able man probably doing a difficult job and his contract must have been drawn up, I guess, when he was appointed in 2008 under Alistair Darling and Gordon Brown.
"I do not know what they were thinking of when they drew it up that way, but it certainly seems to me to be right that the government should step in and sort it out.
Asked what he would have done as prime minister, he said: "I think a state-owned bank should be run on public sector lines."
Downing Street said on Friday morning that David Cameron was "not directly involved" in the process for awarding Hester's bonus.
Earlier Ed Miliband accused the prime minister of a "terrible failure of leadership" over the bonus, which he accused Cameron of "nodding through".
"This is a terrible failure of leadership by the prime minister. For months he's been promising action against excessive bonuses, excessive pay, and now he's nodded through a million pound bonus for Stephen Hester.
"He's also been lecturing shareholders about how they need to show they can get a grip on executive pay. He's the biggest shareholder in RBS. He owns 83% of it through the biggest government, and yet he has let this bonus happen. He's got to come and explain why he's done this," the Labour leader said.
Liberal Democrat foreign minister Jeremy Browne and Labour's shadow business secretary Chuka Ummuna have also voiced their anger at the payout.
But one shareholder, Paul Mumford at Cavendish Asset Management, told the Huffington Post UK that Hester was only paid the "going rate" for doing his job.
"It is one those industries where you do have to give high-powered rewards to get the right people along," he said.
"You're up against an international market as well, with the big American banks which had problems in the past, but where the remuneration packages are quite unseemly."
Tory MP Brian Binley, who sits on the Commons Business Committee, told the Huffington Post UK: "I understand the government's position in that contracts are contracts, the last thing we want is people going to court to argue for their rights.
"I also understand the need to ensure that we attract the really important jobs. But I also understand the need for individuals in important positions that get paid a lot to recognise the difficulties at this moment, the damage the banking sector did to the economy, and I think we want to see bankers acting responsibly.
"I think Stephen ought to recognise these difficulties, and I think a gesture, in the circumstances, would be helpful."
Browne said on BBC 1's Question Time on Thursday night that Hester should "reflect" on his bonus and his earnings, which saw him take home in three days what a soldier fighting in Afghanistan did in a year.
"I think he should reflect on that," the Liberal Democrat minister said.
"He is working for a company which is five sixths owned by us, the taxpayer, and I think he has to think like a public servant, not like someone who's there to line their own pocket.
"He needs to think like a public servant who has a duty to his country, not just his own wealth."
Browne added: "No-one's forcing him to take this money. He could struggle on with £1.2m."
Chuka Umunna, who leaders Labour's shadow business team, said he was "flabbergasted" that Hester had been given a bonus.
He told BBC Radio 4's Today programme: "I don't think I would have paid any bonus in these circumstances."
Umunna said the bonus was issued on an "annual basis" so there was "discretion" able to be applied by the government.
Pay at RBS has become a lightning rod for public fury over huge rewards in the financial sector ever since its £45bn state bailout.
The bank's remuneration committee had reportedly been considering a bonus of up to £1.5m for its highly-regarded leader but Cameron publicly said it should be less.
The decision followed talks with UK Financial Investments (UKFI), the body which manages the taxpayer's stakes in Britain's bailed-out banks.