"The ANC Study Group commends comrade Brown for acting in the interest of good governance," said the chairperson of the group, Zukiswa Rantho, who is also the acting chairperson of Parliament's portfolio committee on public enterprises.
"The ANC has maintained that the decision to reappoint Mr Molefe was reckless after having resigned from the entity following damning allegations against him in the Public Protector’s report."
The portfolio committee earlier this month called Brown and the Eskom to explain to why they decided to reinstate Molefe at the helm of the power utility.
The board claimed that Molefe did not resign from Eskom in November in the wake of the release of the report on state capture but had instead sought early retirement.
However, Rantho said afterwards that MPs were "not convinced" by the explanation.
The ANC's national spokesperson Zizi Kodwa put it more bluntly, accusing the board and the minister of lying, and the ruling party then formally called on Brown to rescind Molefe's reappointment.
On Wednesday, Brown announced that she had asked the board to relieve him of his duties in line with a decision by an inter-ministerial commission.
Finance Minister Malusi Gigaba, who was a member of the commission, said Molefe should not have been allowed to return to Eskom and the mistake had hurt the company and the country.
Rantho said the study group wanted to help Brown to strengthen oversight over public enterprises.
"The ANC Study Group commits to working with comrade Brown to strengthen her oversight role as the shareholder representative in state owned companies and promoting good governance and accountability."