The other woman was also charged with disturbing the peace.
She was told she would have to pay 1,000 kroner (134 Euros) after she refused to remove the veil.
"She chose the latter", Borchersen said.
A spokesperson for group Kvinder I Dialog (Women In Dialogue) told the Independent: "The goal of this demonstration is to show that we do not accept this kind of unjust treatment regardless of who we are dealing with".
The episode took place in the center of Hørsholm center where the woman with niqab came up to top with another woman by an escalator in the center. They're investigating CCTV footage to see if the other woman had deliberately tried to rip off the niqab. The police told the ppaer that nothing indicates that the turmoil arose from the fact that one woman was wearing niqab.
The Danish parliament enacted the face ban in May, joining France and some other European countries to uphold what some politicians say are secular and democratic values.
The fine was the result of a new law banning all face-covering clothing that went into effect on August 1.
Human rights campaigners have slammed the ban for violation of women's rights, while supporters argue the ban enables better integration of Muslim immigrants into Danish society.
Some Muslim women have said that they will refuse to comply with the ban and intend to continue to wear a niqab.
Both women have been charged for fighting in public, but the Muslim woman was also fined for failing to obey the new law. Following this new law, first-time offenders face a fine of 1,000 kroner (around $150) while repeated offenses could lead to fines of up to 10,000 kroner (around $1,500) including a jail sentence of up to six months.
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