- "There is no point in going home until we get justice," Mr Punia told reporters on Sunday night after he was released from detention.
- Footage showed protesters climbing over barricades and being carried away by the authorities.
Police in India's capital Delhi have filed cases including of rioting against the country's top wrestlers after they were detained during a protest.
Olympic medallists Sakshi Malik and Bajrang Punia were among protesters detained on Sunday as they tried to march to India's new parliament.
They were released later in the night.
Police also cleared out their protest site in Delhi, though the wrestlers have said they will return there.
"There is no point in going home until we get justice," Mr Punia told reporters on Sunday night after he was released from detention.
Two-time World Championship medallist Vinesh Phogat and her sister Sangeeta were among the wrestlers who were detained. They and Ms Malik were released on Sunday evening.
Currently, there's no clarity over when and where the wrestlers will resume their protests. A top Delhi police official told media that if the wrestlers applied for permission to continue their protests, they would be allowed to do so at "a suitable place other than Jantar Mantar" - Jantar Mantar is a heritage site in Delhi where the wrestlers had been protesting for more than a month.
"All facilities had been provided to the wrestlers at Jantar Mantar for 38 days, but yesterday they violated the law despite all requests made to them," said Suman Nalwa, deputy commissioner of Delhi Police.
The wrestlers said that they wanted to march peacefully towards the new parliament, but were not allowed to do so. "We didn't riot, we didn't damage any public property," said Ms Malik, who is the only Indian woman wrestler to win an Olympic medal.
The wrestlers began protesting on 23 April, demanding the arrest of their federation chief, Brij Bhushan Sharan Singh, for allegedly sexually harassing female athletes.
Mr Singh, an influential lawmaker and politician from the governing Bharatiya Janata Party (BJP), has denied the allegations and accused the wrestlers of being "politically motivated".
On Sunday, a scuffle broke out between the protesters and the police while Prime Minister Narendra Modi was formally opening the country's new parliament building, which is just a few kilometres away from Jantar Mantar. Police said that the protesters did not follow their directions and that they detained those who tried to break security barricades.
Footage showed protesters climbing over barricades and being carried away by the authorities.
"They broke the law," Dependra Pathak, Delhi's Special Commissioner of Police, told local media.
However, Ms Malik claimed that they had been "walking quietly" and that the police "dragged and forcibly detained" protesters without telling them where they were being taken.
"The whole world is watching how the government is treating its players," Vinesh Phogat tweeted.
On Sunday evening, police filed cases against Ms Malik, Mr Punia, the Phogat sisters and "other organisers of the protest". They have been accused of rioting, assembling unlawfully and of obstructing public servants from doing their duty.
Visuals of the athletes being dragged and carried off in buses went viral, sparking criticism from some top athletes and opposition politicians.
"This makes me sad. There has to be a better way to deal with this", Olympic medallist Neeraj Chopra tweeted in reaction to a video which showed police pulling the Phogat sisters as they sat on the road.
"Why does it have to come down to our wrestlers being dragged around without any consideration? This isn't the way to treat anyone. I really hope this whole situation is assessed the way it should be," said Indian football team captain Sunil Chhetri.
Several opposition leaders, including Congress's Rahul Gandhi and Delhi chief minister Arvind Kejriwal, criticised the police's actions.
The wrestlers began protests in January but they called it off the same month after India's sports ministry stripped Mr Singh of his administrative powers for a few weeks and the government promised to investigate their complaints.
But the wrestlers restarted their protests in April, calling for his arrest.
So far, the police have filed two cases against Mr Singh, including one under India's Pocso (Protection of Children from Sexual Offences) Act - which deals with sexual offences against children.
Mr Singh has said that the law was being misused. He has been questioned by police but not arrested yet.