Muthambi, who was not appointed by the Cabinet to the committee, and Manyi are known to be strong supporters of President Jacob Zuma. Manyi, who is running a campaign in support of the Guptas, is said to have attended in his capacity as an adviser to Muthambi.
Their participation in the meeting with Nedbank adds to questions around the standing of the committee. Finance minister Pravin Gordhan, who was appointed by the Cabinet to participate, refused to do so.
The minister has applied to the high court in Pretoria for a declaratory order that ministers cannot intervene in the relationship between banks and their clients.
The committee was appointed after the country's four major banks ceased doing business with Gupta-owned Oakbay, amid allegations that the family was using its relationship with Zuma to secure business and other favours.
A number of the banks did not agree to a meeting with the ministerial committee as there was uncertainty about the legality of the committee.
In an affidavit supporting the minister's application, Brown detailed the meeting between Nedbank and the committee.
His affidavit included an e-mail in which Brown's personal assistant requested the names and titles of the government officials who had attended the meeting on May 6.
Zarina Kellerman, from the department of mineral resources and secretary of the committee, sent a list of names that included Muthambi and Manyi, and a second adviser, Sandile Nene.
Muthambi's spokesman, Ayanda Holo, on Monday could not immediately respond to questions about why the minister attended the meeting.
Despite Kellerman indicating that labour minister Mildred Oliphant attended the meeting, Brown disputed this in his affidavit. Gordhan was also not in attendance.
The Gupta family sought Gordhan's intervention when the big four banks closed the company accounts.
Brown, in his affidavit, said mineral resources minister Mosebenzi Zwane had assured him the purpose of meeting was "not to represent any particular family or company", but told him about the potential job losses the closing of the accounts would cause. He claimed Zwane had suggested Nedbank consider stepping in to "save jobs" considering that members of the Gupta family had resigned from the companies.
"The overall impressions I came away with was that the purpose of the meeting was to determine whether there was a coordinated decision amongst the major South African banks to terminate the accounts of persons affiliated with the Gupta family, and whether Nedbank would consider engaging with the relevant entities as their primary banker," Brown said.
Nedbank is supporting Gordhan's application on the basis that no sphere of government or minister had the power to intervene when a bank chose to terminate its relationship with a client. If the government were allowed to intervene it would have "severe prejudicial consequences" for banks and for SA in general, Brown said.
"Government has no competence in law to interrogate why a bank terminated its relationship with a client in general, or to inquire whether a bank has terminated its relationship with a client in order to give effect to antimoney laundering legislation and antibribery and corruption legislation in particular."
