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After a meeting that lasted seven hours, Mr Thakur, flanked by some of India's most celebrated wrestlers, in a news conference assured that the government will support the wrestlers at every step of their battle.
"An oversight committee will be set up. It will take four weeks to give a report. Any allegation, whether sexual harassment or financial wrongdoing, we will dive deep and investigate them. We will take action after that," Mr Thakur said.
After meeting Mr Thakur, the wrestlers called off their protest against alleged sexual harassment and misappropriation of funds.
"Till the time the investigation is not complete, a committee will see to the day-to-day working (of the Wrestling Federation of India)...I thank the athletes for speaking to me," Mr Thakur said.
Olympic medallist Bajrang Punia said the minister has assured he is with the wrestlers at every step. "Prime Minister Narendra Modi has also always supported our athletes," Mr Punia said.
The Indian Olympic Association has also announced a seven-member panel to investigate the allegations against Mr Singh. The panel will have noted athletes Mary Kom, Dola Banerjee, Alaknanda Ashok, Yogeshwar Dutt and Sahdev Yadav as members.
Mr Singh has denied the allegations and refused to resign. "If I speak, there will be a tsunami...I am not here because of someone's charity. I have been elected by the people," he told reporters in Uttar Pradesh's Gonda.
Earlier, Mr Thakur had dialled Mr Singh and cautioned him against making any statement to the media.
Ahead of the meeting on Friday night, the wrestlers had sent a letter to PT Usha, the head of the Indian Olympic body, seeking action against Mr Singh.
"Vinesh Phogat was mentally harassed and tortured by the WFI chief after she missed out on an Olympic medal in Tokyo. She almost contemplated suicide," the wrestlers wrote in their letter to Ms Usha, adding "they fear for their lives". Ms Phogat has agreed to reveal the identity of the sexual harassment survivors to the Indian Olympic Association committee.
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