Mr Darling said ministers only became aware last week that a decision by the bank's former board to allow Sir Fred to take early retirement had increased his pension entitlement and might have been a "discretionary choice".
UK Financial Investments - the body which manages taxpayers' shareholdings in the part-nationalised banks - has been asked to look into clawing back some of the pension deal, the Chancellor told MPs, but Sir Fred could end the controversy by agreeing to give it up.
"The ball remains in his court," Mr Darling said.
The news followed calls from shadow chancellor George Osborne for the Government to reveal how much it knew about Sir Fred's pension deal.
He also called for Sir Fred to give up the pension, saying: "There is of course now only one person who can correct this huge error of judgment by the Chancellor, and that is Sir Fred Goodwin himself, who should in all decency renounce his pension."
Mr Osborne described the pension as a "totally irresponsible use of taxpayer's money" and said there appeared to be differing accounts on how much the Government knew about it.
While Mr Darling had said the Government only found out about the deal recently, present RBS chief executive Stephen Hester had told BBC Radio 4's Today programme: "The arrangements for my predecessor's departure were negotiated directly between past directors of this board and the Government and him."
Responding to a statement announcing the latest bailout for RBS, which will see £325 billion of the bank's assets placed in a taxpayer-backed protection scheme and a further £13 billion stake in the institution taken by the Government, Mr Osborne asked "who exactly" knew about the deal.
He also wanted to know whether Sir Fred, who presided over the near collapse of RBS, had delayed his departure to negotiate the pension.
"Whichever way one looks at it, this obscene pension is unacceptable and the Government is on the hook," Mr Osborne said.
"Either they did know and failed to act, or didn't know and failed to ask the right questions.
"It is a totally irresponsible use of taxpayer's money, and there is of course now only one person who can correct this huge error of judgment by the Chancellor, and that is Sir Fred Goodwin himself - who should in all decency renounce his pension."
Mr Darling agreed it was "beyond doubt" that most people would find it hard how the former boss of a bank that had posted the biggest losses in UK corporate history could be paid "such an enormous pension" from the age of 50.
But he said: "This agreement was not negotiated by the Government, nor was it approved by the Government - nor would it have been, because the agreement in relation to the remuneration, the pension arrangements between employees of a bank are a matter between that employee and the board of directors.
"What we did know last autumn was that we were told there was a contractual agreement between the board of the bank and Sir Fred.
"What we did not know, because we had previously understood that his pension arrangements were an unavoidable contractual commitment, what we didn't know, and it was only very recently that we became aware, that the decision of the previous board to allow Sir Fred to take early retirement had the effect of increasing his pension entitlement and that that might have been a discretionary choice."
Pressed by seated MPs as to when ministers became aware, Mr Darling said: "Last week, actually, it became clear that this may have been a discretionary choice."
UKFI would continue to discuss with the board of RBS whether the pension could be clawed back, he said, and Sir Fred had been asked to give it up.
Liberal Democrat economic spokesman Vince Cable said he "totally agreed" with Mr Osborne's comments.
"This is public expenditure," Mr Cable said.
"This is a massive public spending increase, public wages, for which there is no justification whatever."
Left-wing Labour veteran Dennis Skinner (Bolsover) said the banking fraternity had been "on a winner" for some time and were no better that Nick Leeson, the rogue trader who caused the collapse of Barings Bank in the 1990s.
He said: "Instead of paying out these vast executive bonuses and Freddie Goodwin's massive £650,000 pension, why not tell them that those of us on these benches will gladly walk through that voting lobby to ensure that all those executive bonuses and all that pension fund for Freddie Goodwin and his mates will be paid for out of the toxic debt when it had been repaid - and that will be never.
"That's the proposal we ought to put to these bankers, and treat them with the contempt they deserve."
Mr Darling said he agreed that it "absolutely essential" to change the culture within banks towards one that ties bonuses to long-term performance.
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