At the time Mr Mandelson was condemned for misleading his building society, by not declaring the loan on his mortgage application.
The move comes after Mr Robinson accused Mr Mandelson of misrepresenting the way his notorious loan was obtained.
The Northern Ireland secretary has always maintained he did not ask Mr Robinson for the money.
Shadow Trade and Industry minister David Heathcoat-Amory has called for the affair to be reinvestigated by the Commons watchdog, which originally examined the loan two years ago.
In a letter to the chairman of the Standards and Privileges Committee, he states: "It is clear that Mr Mandelson and Mr Robinson differ in their version of how the loan arose. They cannot both be correct.
"It would be a serious matter if Mr Mandelson was untruthful or misleading in the evidence he gave to the committee on 18 May 1999. Yet that is the clear implication of Mr Robinson's version of events."
The millionaire Labour MP told the BBC he stood by claims in his book that Mr Mandelson is a "divisive and destabilising figure".
But a spokesman for Prime Minister Tony Blair played down the affair as "pretty flat froth".
He said: "We are far more interested in tackling issues such as crime, education, health and the economy."
At the time Mr Mandelson was condemned for misleading his building society, by not declaring the loan on his mortgage application.
He resigned from the Cabinet in December 1998, but returned to the front bench 10 months later. Mr Robinson also quit his office and remains on the backbenches.
He told BBC Radio 4's Today programme he was not accusing Mr Mandelson of lying, but that there was clearly a "marked difference of opinion" between them.
Mr Mandelson's account of the affair "did quite frankly imply that I put him up to it in some sort of way, gave the impression that I might be the sort of person who might use my means, my money, to buy influence, power, even office".
But Mr Mandelson hit back immediately, insisting he had never "suggested or implied" the loan had been forced on him.
He said he now considered the whole matter closed.
Mr Robinson said the subject first came up at a dinner in 1996, when Mr Mandelson spoke of needing help to buy a residence in Notting Hill and he replied he could help if necessary.
"The next morning at nine o'clock the phone rang and it was Peter saying quite openly 'would you really help me buy a house', to which I replied 'yes, if that's what you want'.
"I think the fact that he re-initiated the discussion the following day shows that it was really Peter that was taking the lead in these matters and scotches any idea of my trying to put him up to it," he said.
'No ill will'
Insisting he personally bore Mr Mandelson no ill will, Mr Robinson said that at the same time the Northern Ireland secretary played a role "that isn't always conducive to the administration of good government".
He had a way of "re-opening" issues in public that had already been settled by the government, such as Europe.
Speaking immediately after the comments had been broadcast, Mr Mandelson said that Mr Robinson had "volunteered his financial help if needed".
"I later took him up on his offer and I was grateful to him.
"I have never suggested or implied that he forced a loan on me. Nothing would be more ridiculous."