The row occured after the Freedom Front Plus (FF+) alleged that advocate Simmy Lebala had drafted a false statement in a previous civil case, and so was unsuitable to act as witness leader for the commission.
FF+ defence spokesperson Pieter Groenewald accused Lebala of "committing perjury" and said the party would be lodging a complaint against him with the bar council.
Commission spokesperson William Baloyi said Groenewalds statement was based on a misrepresentation of facts and was false.
Groenewald referred to a case in the North Gauteng High Court between Tasima, which runs the Electronic National Administration Traffic Information System (eNatis), and the department of transport, in which Lebala had acted for the state.
"It was found that the respondents lawyer had committed perjury in terms of a statement and the court recommended that the lawyer should be investigated by the law society of the Northern Province," Groenewald said.
He added that Lebala had acknowledged he was responsible for the drafting and content of the affidavit in question.
"It is clear that Lebala does not hesitate to draft false statements for witnesses. Lebala is not suited to act as witness leader for the commission and should immediately be removed," said Groenewald.
Baloyi denied that the attorney who had briefed Lebala and attested to the supporting affidavit has been convicted of perjury.
"Although a complaint was indeed lodged against him with the law society of the Northern provinces, it related not to perjury but to other ancillary issues relating to the matter," Baloyi said.
He added that Lebala had neither attested to the affidavit nor given evidence on the issue and could therefore not have committed perjury.
"Lebala denies that he accepted responsibility for drafting the affidavit and for its contents. All he acknowledged was that he had acquainted himself with the affidavit, as indeed he had to as counsel who argues the matter for the respondent," said Baloyi.
On a mission to build a positive image after a string of negative media reports, the commission, chaired by Judge Willie Seriti, started its public hearings on Monday almost two years after it was set up.
Several controversies relating to high-profile resignation of key senior staff, questionable appointments and allegations that it is pursuing a "second agenda" have dogged the commission since its inception.
Two senior South African navy officers, Rear-Admiral Rusty Higgs and Rear-Admiral Alan Green, testified for three days this week.
They were not cross-examined, as no one came forward when Judge Seriti asked the commission if anyone would like to question them.
The commission was taken back to when the first frigates were bought in 1977, and told that no equipment had been purchased because of the international embargo against South Africa during the apartheid years.
Green said the navys fleet was ageing and in dire need of maintenance when the democratically elected government came into power in 1994.
The commission heard about the 1996 South African white paper on defence and South African Defence Review of 1998, which informed Cabinets decision to approve the "strategic defence procurement package" the arms deal.
Parliament approved the decision after a public consultation process, Higgs said. "The people of South Africa had spoken."
Green on Wednesday dismissed criticism by anti-arms deal campaigner Terry Crawford-Browne that the equipment purchased during the deal is not currently in use.
He denied that he made a statement to a parliamentary portfolio committee that the equipment is not in a functioning condition.
Higgs denied that the equipment is not working and gave examples of where it had been used in recent years.