The latest figures showed that, in the six years since the world record £45bn bailout was made to save the Edinburgh-based bank, an equivalent sum has been lost.
After the losses were announced, RBS shares fell by 8%, wiping £1.7bn off the bank's stock market value.
While Ross McEwan, the RBS chief executive, insisted the bonuses were necessary to retain and attract the best staff, they sparked a wave of anger, with one critic saying RBS now stood for the "Robber Banking Service".
The bank boss said: "I understand it is a highly emotional issue to see bonuses paid when we are still losing money. The issue for me as a pragmatic executive is that I need to be able to pay what it takes to actually get people to do the job for us."
He added: "When you look at RBS, we of all banks have been the one who have been pulling the pay and bonus structures down but I do need to be in the market to get people to do these jobs."
Mr McEwan pledged to rebuild trust in the group with a radical overhaul that would slash costs by £5bn within three years and turn seven divisions into three.
He warned of further job losses but insisted the moves were necessary to nurse the group back to health and create a "smaller, simpler and smarter" bank.
But Vince Cable, the business secretary, led the criticism. "The public will simply not understand why big bonuses and large salaries continue to be paid out by a loss-making public enterprise, still under-performing in many areas," said the LibDem frontbencher.
"The smaller bonus pool is due to the bank's US-based investment banking operations, which will soon be sold. If RBS is to become the sensible, boring bank envisaged by the CEO, the bonus culture will have to go," he added.
His colleague, Lord Oakeshott, the party's former Treasury spokesman, said loss-making firms in other industries would not pay such large bonuses. "They've lost £8.2bn of our money and they've paid £576m in bonuses; what on earth would they pay if they made a profit? What does RBS stand for? Robber Banking Service?"
The LibDem peer added: "That's the economics of the mad-house. No normal business making a thumping loss like this would pay out massive bonuses. Banking is just on another planet. Wherever you look, RBS is a total disaster."
Francis O'Grady, General Secretary of the TUC, added: "The multi-million bonus pool at RBS would be better spent getting the bank back into good shape and repaying taxpayers rather than on boosting the already inflated bank accounts of its senior staff."