25 November 2013 Last updated at 16:30
RBS has asked law firm Clifford Chance to investigate claims it forced firms to close so it could make a profit.
Two reports published on Monday criticised the bank for its treatment of small firms, claims which Chancellor George Osborne described as "shocking".
Clifford Chance will look into the allegations contained in reports by Sir Andrew Large and Lawrence Tomlinson.
RBS said in a letter to Sir Andrew that the bank had in many areas fallen short in its treatment of customers.
Andrew Tyrie MP, chairman of the Treasury Committee, said: "The reports published today make clear that there is a fundamental cultural problem with RBS's lending to and treatment of SMEs [small and medium enterprises].
"This is unwelcome but not wholly surprising. It confirms what my parliamentary colleagues and I have been hearing for a number of years and which was, at various times, vigorously rebutted by RBS."
'A tough read'
Sir Andrew Large's report, commissioned by RBS, looked into the bank's lending to small businesses. It said that the bank must tackle some "serious allegations" by a small number of firms.
The Tomlinson report, set up by Business Secretary Vince Cable, said there was evidence that the bank deliberately put some "good and viable" businesses into default so it could make more profit.
Mr Cable has passed the Tomlinson report to City regulators, the Financial Conduct Authority and the Prudential Regulation Authority.
Ross McEwan, RBS chief executive, said in his letter to Sir Andrew that the report by the former Bank of England deputy governor had "been a tough read".
He said that RBS had already put in place new procedures to improve lending to small firms and halt "the reckless lending practices that broke this bank five years ago".It is not altogether surprising, given the scale of the mess, if RBS succeeded in doing over and doing in some business that did not deserve it
"Your report also highlights that when times are tough for our customers, some have said they were angry about the treatment they received," the letter said.
Although Mr McEwan did not refer directly to the Tomlinson report, the company added later that the allegations were not "something that Clifford Chance would ignore".
Mr Cable told the BBC that the evidence compiled by Mr Tomlinson looked "solid". In a television interview with ITV, Mr Osborne said the allegations were "shocking" and would not be "brushed under the carpet".
The Tomlinson allegations centre on the bank's Global Restructuring Group (GRG) lending division, which specialises in handling loans seen as being more risky.
The Tomlinson report says that putting a business into the GRG generated revenue for the bank through fees, increased profit margins and the purchase of devalued assets by their property division, West Register.
The practice of removing a bad debt from a bank's books is not an unreasonable one, particularly as major lenders have been trying to move away from riskier assets.
But Mr Tomlinson told the BBC that there was a perception among small businesses that they were being "purposefully distressed" in order to get them into the GRG, which, even if wrong, should be addressed by RBS.
Mr Cable said his department would not take the report at "face value", but added: "We are pretty confident that the evidence is solid."
But he added: "I am, however, confident that the new management of RBS is aware of this history and is determined to turn RBS into a bank that will support the growth of small and medium-sized businesses."
Mr Tomlinson, an entrepreneur, acted independently of government in producing the report, and did not set out to look solely at RBS.
But he said what he had uncovered through talking to businesses had put RBS and its GRG into focus.
He also said conversations with affected businesses had made a big impact on him.
"I feel really sick sometimes. It is really disturbing," he said.
"It is ruining people's businesses for sure, and in some cases having a huge impact on their personal lives too, even leading to family breakdown."
He told the BBC later that he had uncovered some "horrific stories" suggesting that the conduct at RBS was "systematic and institutional".
The report found:
The bank said in a statement: "In the boom years leading up to the financial crisis, the overheated property development market became a major threat to the UK economy.
"RBS did more than its fair share to fuel this and commercial property lending was one of the key drivers of our near collapse as valuations rapidly plummeted.
"Facing up to these mistakes has been a difficult, but essential part of making RBS a safe and strong bank once again."
The shadow business secretary, Chuka Umunna, said: "The claims made by Lawrence Tomlinson against RBS' Global Restructuring Group are extremely serious indeed."
Sir Andrew Large's report said there had been confusion over RBS's lending objectives and strategy.
The bank must "ensure clear and simple lines of responsibility, and reduce organisational fragmentation," the report said. Currently, lending is split across several divisions.
RBS, 81%-owned by the government, is the UK's biggest lender to small firms. Mr McEwan pledged in his letter that RBS would write to thousands more businesses setting out how much more the bank was willing to lend them.
It had already offered £4bn in this way, and this would go up to £10bn, he said.