Labour peer Lord Foulkes has written to the FSA over whether RBS non-executive directors were pressurised into not questioning some of its risky policies.
He has asked FSA boss Lord Turner to investigate whether the bank made knowingly false statements to investors about how secure its position was.
Lord Turner told the BBC's Andrew Marr Show he had received the letter and would be looking into the allegations.
He also said the watchdog's hands were tied over Sir Fred Goodwin's pension.
RBS was bailed out by the government in October 2008 and taken into 68% public ownership.
Referring to Lord Foulkes' letter, an RBS spokesman said: "We are not aware of any evidence to support such a claim and it is not an issue that has been raised by any non-executive director past or present with the company or indeed with the FSA who are in regular dialogue with the board and its members.
"If Lord Foulkes has any evidence to support the assertion it would be in the interests of all parties if he shared it."
Lord Foulkes wants the FSA to investigate whether the bank made knowingly false statements to investors about how secure its position was and whether there was "intimidation" of non-execs.
He wants to know "whether any knowingly false statements were made or prospectuses issued that could have led potential investors or depositors to believe the position was more favourable than the board knew it to be".
Chairman of the FSA, Lord Turner says Sir Fred Goodwin's pension is a "matter for the government"
Speaking to Andrew Marr, Lord Turner confirmed he had received Lord Foulkes' letter and would be looking into the allegations, but said he could not comment on the issues raised.
Lords Foulkes said if either of the allegations were true then the FSA would have no option but to exercise its power in pursuing any of those suspected of being involved through the criminal courts as a matter of urgency.
He said: "There is widespread public anger among the public and in Parliament that bankers in the midst of this financial crisis appear to be profiting and no action is being taken in relation to action which could constitute criminal offences."
In his letter to the FSA Lord Foulkes, a former minister in Tony Blair's government, calls on the FSA to interview all non executive directors about the claims.
Former non-executive members of the RBS board were paid £72,500 a year and required to "satisfy themselves on the integrity of financial information and that financial controls and systems of risk management are robust and defensible".
BBC business correspondent Joe Lynam said he understood Lord Foulkes had not spoken directly with RBS non-executive directors but received the allegations through intermediaries.
"This just adds to the mounting canon of bad news surrounding RBS," our correspondent added.
Meanwhile, the FSA said it could only claw back some of Sir Fred Goodwin's controversial pension if legal offences had been committed.
There has been an outcry over the ex-RBS boss's £16m pension pot, particularly as the bank is now taxpayer supported.
Lord Turner said the FSA could only take action over issues of misconduct, not "misjudgement".
Despite a clamour from commentators and politicians from all parties, including the prime minister, Sir Fred has so far refused to offer any commitment to return part of his pension, which is worth £703,000 a year to him.
"We can go after people legally if they have committed legal offences," Lord Turner told the BBC.
"But that has to be things where they have hidden information, failed to provide information.
"A misjudgement, whether it be a business misjudgement or whether it be what I think most people think that Sir Fred Goodwin's committed - which is a misjudgement in not being willing to give back some of his pension - those are not legal issues for the FSA."
However, he said that the appropriate sanctions for misconduct would not normally include sequestering a pension.
Last week it was revealed that British pension funds are looking to sue Sir Fred and RBS in US courts.
They allege RBS and Sir Fred "falsely reassured" investors that the bank was in good health when it was "effectively insolvent" because of bad loans.
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