Britain's second-biggest bank made the plea with "a great deal of humility", according to its chairman, Sir Tom McKillop, as the Edinburgh-based group revealed that a further 5.9 billion was to be written off, from risky property-related assets in the United States.
It came as mortgage lenders warned the government that interest rates for new borrowers were unlikely to come down, despite intervention by the Bank of England earlier this week.
Some of the UK's biggest mortgage lenders, who met Alistair Darling, the Chancellor, yesterday, are understood to have told him that the cost of deals for new borrowers was likely to stay high for the foreseeable future.
However, lenders also pledged to do more to help homeowners who got into difficulties keeping up with their mortgage repayments.
The Bank of England on Monday unveiled a 50 billion scheme to help tackle the problems caused by the credit crunch, under which banks can swap their riskier mortgage-backed assets for safer government bonds, in a bid to kick-start the crippled money markets.
There were unconfirmed reports that Sir Fred Goodwin, the RBS chief executive whose 4.2 million pay package last year included a 2.9 million bonus, offered to resign before the rights issue was finalised. He is due to face shareholders at the company's annual meeting in Edinburgh today.
But yesterday, he was given the strong backing of Sir Tom, who said: "The board unanimously believes that our executive team have all the ability to steer the bank successfully through this tricky period."
In a remarkably candid statement, Sir Tom declared he was "pretty confident" the rights issue would be well-supported.
"These are large sums," he said. "This is a big ask for our shareholders. We come to ask that with a great deal of humility.
"You should be in no doubt about the degree of contrition. This is a significant set of announcements.
"There is no single individual responsible for these events. To look for a sacrificial lamb just misses the whole plot."
Rival banks Barclays and Halifax Bank of Scotland are seen as likely to be next to follow RBS's bid to bolster its balance sheet.
Mortgage rates are governed by the inter-bank lending rate, Libor, which is currently at 5.90 per cent, 90 basis points above the Bank of England 5 per cent base rate, compared with a historical average of only 13 points above. Lenders will not be able to pass on lower rates to customers until Libor rates come down, and this is expected to take some time. At the same time, lenders are trying to increase their margins in the face of anticipated higher levels of arrears and falling house prices.
Yesterday's discussions between the Chancellor, Caroline Flint, the housing minister, and key members of the mortgage industry, including Michael Coogan, the director-general of the Council of Mortgage Lenders (CML), focused on what lenders could do to help borrowers who run into problems.
Both the CML and the Finance and Leasing Association agreed to review their voluntary codes on treating customers fairly and to report back to ministers by the end of next month.
The industry trade associations said they would meet consumer groups as soon as possible to take their views into account. Lenders also said they would repossess homes only as a last resort, while they would continue to meet all statutory and voluntary commitments on treating customers fairly.
They also said they would look at new voluntary activities, such as strengthening links with debt advisers, providing updated debt information and pro-actively identifying borrowers at risk of facing repossession.
The government said it would work with the industry to keep under review the framework for helping borrowers who end up in difficulties.