The civil rights group said an independent panel would now investigate the assertions made against Motsepe by some women staff at the organisation.
The women would be offered counselling in the interim, according to Equal Education.
The organisation’s Yoliswa Dwane had, in a statement last month, said the allegations were disclosed to members of the organisation's senior management team.
“A preliminary investigation was conducted and a formal complaint was then submitted to EE’s National Council, our movement's highest decision-making structure, on April 24. On that day it resolved that a panel was to be appointed which assessed the allegations,” said EE.
EE said it was making a public statement “in the interest of openness and transparency” and was determined to act with integrity and sensitivity.
Motsepe had tendered his resignation on April 25.
He has not accepted wrongdoing at this stage, and the National Council has resolved to continue with the appointment of an independent panel to investigate the allegations.
“We have been deeply distressed by these developments. We are resolute in our commitment to dealing with this matter in a just and transparent manner,” said EE.
On Tuesday Motsepe said he was shocked when informed of the allegations on April 24.
“They read out the accusations and questioned if I had told staff members to leave their husbands and be my second wife, or given a staff member the cold shoulder because they rejected my offers of romance. Or if I fired anyone because they refused to do something."
He said he took the decision to resign after being pressured by some members who, he alleged, said he was making the complainant uncomfortable.