As per Tokyo Games bronze medallist Bajrang, they withdrew their protest after the government assured that no one related to Brij Bhushan will contest the polls.
India have won five bronze medals so far in wrestling in this edition.
Vinesh's outburst comes after the United World Wrestling provisionally suspended the Wrestling Federation of India for not conducting elections on time.
Around 150 people, including family members of the wrestlers, are seeking a meeting with IOA president P T Usha and ad-hoc panel chief Bhupender Singh Bajwa.
The move to exempt Bajrang and Vinesh, however, has not gone down well with fellow competitors, who have threatened to move court.
Bajrang, in a live social media address, had claimed on Saturday that Yogeshwar several times asked him to lose bouts on purpose in the past.
The protesting wrestlers have been invited by the government for the second time days after they met Home Minister Amit Shah.
He further said the protest has not died down and that they are strategising on how to take the movement forward.
Both Sakshi and Bajrang have denied the reports of withdrawing from the protest.
The Delhi Police had beefed up security at Jantar Mantar following protesting wrestlers' call for a 'Mahila Samman Mahapanchayat' before the new Parliament building on Sunday.