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.
"People will be at a loss as to why somebody can get a whacking great bonus like that when they're basically running a government concern, and I'm at a loss to understand why this has happened. "If you're going to have a Government institution like that, there should be a concept of service and a concept of duty to the wider British public who stepped in to bail out that bank in 2008."
"I don't think anybody blinked. In the end the shareholders make their views known, and the government made its view very strongly known that the bonus should be much lower than last year. But in the end the board has a contract with its chief executive and it has to assess whether it met the various benchmarks there. "Now, we need the board, we need the chief executives to turn this bank 'round. It failed before, do you remember, and it's still at risk. We've got to get our £43bn out. And Stephen Hester and his board are the people we're trusting to do that, and that's why we've put in place the various financial and remuneration arrangements that were there in the original contract."
"So much for Cameron's talk of moral capitalism, a bonus of this size is utterly immoral. A £1 million reward - on top of a salary of more than a million - is unjustifiable given the job cuts at RBS, the missed lending targets and the dip in the company's share price. "£1 million could be better spent keeping nurses on wards, keeping Sure Start and day centres open. It is wrong that the bankers who created the financial crisis are getting huge bonuses, while public service workers face frozen pay and job cuts, and are struggling to make ends meet. "The Prime Minister needs to prove he's serious when he says we're all in it together by making Stephen Hester turn down his bonus."
"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."
"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."
"Ministers have spoken of the need for greater shareholder activism but despite the Government being the largest shareholder in RBS, have failed to rein in excess. People will not be able to understand why, at a time when they are facing the biggest squeeze on their incomes in a generation, the Prime Minister has failed to act despite his promises to do so. "The Deputy Prime Minister, Prime Minister and others have tried to suggest that the bonus framework was set by the last Labour government which is simply untrue. RBS has been very clear that the remuneration committee of the board of the bank had discretion in this case."
"I have a lot of sympathy with that Jeremy Browne said on television last night. There are some bankers who have decided not to take a bonus this year like the chief executive of Lloyds. It is up to Stephen Hester, that is his decision. "The Chancellor and the Treasury have explained the frustrating realities of all of this, which is that if we ripped up the contracts that the Labour government have signed with them or changed the arrangements that manage our stake in the banks, the taxpayers would have ended up paying even more money. There are some frustrating realities to this, but Mr Hester needs to make his own decision. "I have a huge amount of sympathy with peoples' sense of dismay when they see these figures. They are seeing figures from another planet. There are these realities and these constraints and it is for each individual to make up their own mind."