Only one of the women, 17-year-old gymnast Maedeh Hojabri, has been identified.
Her account has since been suspended, but the BBC reports that many others are re-posting her videos on social media sites (see some examples here and here) as well as posting their own dancing videos in protest.
"It wasn't incitement, I didn't want to encourage anyone, I didn't have an objective", she said.
Hojabri, who reportedly has often spoken about gymnastics and parkour in her videos, was not wearing a hijab in the videos that got her into trouble, which is required by law for women in the authoritarian country.
July 9, 2018-Forcing a teenage girl to confess on state TV for the "crime" of posting a video of herself dancing on Instagram represents a blatant violation of freedom of expression and demonstrates the extent to which the authorities are brutally imposing their cultural dictates on the people of Iran. According to Shabooneh, a local news website, three other individuals were also released on bail after receiving similar charges. "I'm dancing for liberty and joy, which are your right", said one middle-aged woman who posted a video of herself dancing in her living room.
Hojabri has around 300 videos on her Instagram account, many of which show her dancing in both Iranian and Western styles.
"I didn't work with a team, I received no training".
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"In April, the judiciary arrested a senior Iranian official after a video posted online that showed young boys and girls dancing in public in the northeastern holy Shi'ite city of Mashhad for undermining public decency".
Iran has already blocked access to many social media sites, including Facebook, Twitter, YouTube and the Telegram messaging app. Millions of Iranians continue to use the sites through proxies and VPNs. Meanwhile, the police said they plan to shutdown accounts similar to Hojabri's one.
There has been widespread outcry over the arrest of Hojabri and the other detainees among Iranians in Iran and overseas, by artists, journalists, activists, politicians and thousands of ordinary citizens on social media.
Thousands of Iranians reportedly took to Tehran's historic Grand Bazaar one week ago, forcing its shutdown in protest over the Islamic Republic's decision to spend money on Iran's adventurism overseas instead of helping fuel its troubled economy at home, where over 40 percent of its population is unemployed.
Numerous women took to social media with videos of themselves dancing, declaring "dancing is not a crime".