Andrew Tyrie MP is to write to the bank's chairman Sir Philip Hampton, and discuss the matter in the committee after the summer recess.
That comes after the bank submitted "additional comments" following oral evidence given at the committee last month by deputy chief executive Chris Sullivan and Derek Sach, head of the bank's controversial Global Restructuring Group.
In a letter to Mr Tyrie and the committee, Mr Sullivan says he accepts that the GRG was indeed a profit centre, as described by Sir Andrew Large in his report on RBS's small business lending last November.
A profit centre is an accounting term which means a part of a business that is accounted for on a standalone basis.
Mr Tyrie said: "RBS had not objected to the term 'profit centre' when given extensive opportunity to comment on drafts of Sir Andrew's report last year.
"Yet it decided to contest the term in evidence to the committee, not only in a written statement in February, but also repeatedly in its public hearing in June.
"Following the committee's decision to write to Sir Andrew Large for clarification, RBS has now offered the committee what it euphemistically describes as 'additional comments'. In fact, they have done a belated U-turn."
In his letter, Mr Sullivan says it was "indeed the case that the financial performance of GRG was monitored" which was a "standard accounting practice across all sectors of our business". He goes on: "However, what Mr Sach and I were taking issue with is the way others have used Sir Andrew's report to suggest that GRG had a profit motive with a prejudice against our customers, rather than a turnaround motive."
According to the letter from Mr Sullivan, GRG has recorded a substantial loss over recent years.
But Mr Tyrie said: "It's not as if the facts have changed. So it now appears that RBS has been wilfully obtuse with the committee.
"If this is how RBS deals with a parliamentary committee, how much can customers and regulators rely on it to be straightforward with them?"
Mr Sullivan had also responded to the committee on the extent of the bank's input into the conclusions of the report by its legal adviser Clifford Chance into the workings of the GRG, which the bank claimed "cleared" it of most accusations in the independent Tomlinson report.
Mr Sullivan, who is leaving RBS next year, had previously indicated he had not seen the report before it was published. Now he has confirmed he did see a draft but any input from bank executives was confined to "the correction of facts, typographical errors, suggested points of clarification and changes to syntax", not all of which were accepted.