Many of the ANC applicants, including a number of cabinet ministers, were granted amnesty on the basis that they accepted collective responsibility for offences committed by members of the organisation's structures.
Most of the applications did not specify the incidents for which amnesty was being sought.
Both the National Party and Democratic Party on Tuesday criticised the TRC's handling of the applications.
NP leader Marthinus van Schalkwyk accused the TRC of breaking the law in granting what he called "illegal backroom amnesty" to ANC leaders, and said it faced its most serious credibility crisis yet.
Van Schalkwyk said the commission's founding act specified that amnesty could be granted only to applicants who had made a full disclosure of all relevant facts on a specific offence. It did not provide for a general or blanket amnesty.
The TRC had only two options - either to withdraw the amnesty granted to the ANC leaders and apply the act evenhandedly, or to ask for a change to the act to allow any South African to apply for this kind of soft amnesty.
Van Schalkwyk said he was seeking a meeting with TRC chairman Archbishop Desmond Tutu to discuss the controversy.
"We are trying to finalise a time to suit both of us early next week, so I can hear from Bishop Tutu himself what is going on here."
He also released a copy of a letter sent to the TRC on Tuesday requesting all documentation relating to the applications and the reasons for granting amnesty.
On Monday, NP officials collected copies of the ANC amnesty applications from the TRC's Cape Town offices.
Van Schalkwyk's statement followed newspaper editorials on Tuesday calling on the amnesty committee to explain how it had arrived at its decision to grant amnesty to the ANC members, as well as to Tutu's son, Trevor.
Trevor Tutu was granted amnesty for his conviction arising out of a bomb threat at East London airport in 1989.
In its editorial, the Afrikaans daily Die Burger said the TRC had, in effect, granted a blanket amnesty to ANC leaders.
"This reinforces serious suspicions over the aim and usefulness of the TRC," it said.
The Business Day said the amnesty committee's integrity had been called into question by its "thoughtless" handling of Tutu's application.
"In the public mind there is no prima facie evidence, and there never has been, that Trevor Tutu's motives were in any way political.
"For the sake of its credibility, and for the entire truth and reconciliation process, the amnesty committee owes South Africa an explanation of its finding."
However, the amnesty committee on Tuesday made it clear it was not prepared to be drawn into any public debate.
Committee chairman Judge Hassen Mall stood by the committee's decision to grant amnesty to the ANC members on the basis of collective responsibility, committee executive secretary Martin Coetzee told Sapa.
The decision was taken by Mall and fellow judges Bernard Ngoepe and Andrew Wilson.
Coetzee said the judges had considered the applications in conjunction with a declaration in which the applicants assumed collective responsibility for all offences and omissions by members of ANC structures.
The committee had also taken into account the ANC's submission to the TRC on the armed conflict, and the requirements for amnesty in the TRC's founding legislation.
In its reaction on Tuesday, the Democratic Party questioned the committee's refusal to explain how it had arrived at its decision on the ANC applications.
"In our view, the collective amnesties will now inevitably be taken on review to a court of law by a party which has locus standi, namely an interest in the decision," said Dene Smuts, the DP's spokeswoman on the TRC.
"A person cannot be indemnified for nothing in particular and everything in general unless the law allows for general amnesty, which it does not."