Human rights campaigners slammed the ban as a violation of women's rights, while supporters say it enables better integration of Muslim immigrants into Danish society.
Fines will range from 1,000 Danish crowns ($160) for a first offence to 10,000 crowns for a fourth violation.
Women in niqabs at the protest in Copenhagen held banners reading "Liberal hypocrisy" and "Stop harassing Muslims".
The ban, which the Danish government enacted in May, affects all form of face veils, including burqa, niqab, full-face balaclavas, hats, caps, scarves, masks, helmets, full-length suits and artificial beards. Demonstrators marched from the central district of Norrebro to Bellahoj police station on the outskirts of the capital, where they formed a human chain.
Police said protesters who planned to fully cover their faces at the demonstrations would not risk a fine.
Opponents have said the ban is religious discrimination.
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Et d'avertir: " Jusque-là, le fardeau des sanctions ne sera que de plus en plus lourd si le régime ne change pas de voie ". Certains des principaux alliés européens des États-Unis travaillent depuis ce retrait à empêcher l'accord de se déliter.
It is estimated that Muslims account for about 7 percent of Denmark's population of 5.6 million.
Under the law, the police will be able to instruct women to remove their veils or order them to leave public areas.
"I don't think there are many who wear the burqa here in Denmark".
The British newspaper "the guardian" notes that in political circles, particularly in the Danish party "Venstre" refer to such headdresses as the veil, the burka and the niqab, too harsh to be worn by women in the society.
"Everybody wants to define what Danish values are", said Meryem, 20, who was born in Denmark to Turkish parents and has been wearing the niqab since before meeting her husband, who supports her right to wear it but feels life could be easier without.
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The pastor denies the charges while United States officials have publicly insisted that Brunson is innocent and should be freed. Brunson is being tried on espionage and terror-related charges, which he and the US government vehemently deny.
"To wear the niqab is a spiritual choice and now a sign of protest", she said.
"I've realised that democracy doesn't work".
The 21-year-old added she wants to educate politicians to show they're actually strong and independent women fighting for their right to keep wearing the veil.
"I have come to the realisation that Muslims don't have the same rights as others. So much of politics is hypocritical". The ban went into effect on Wednesday.
Very few Muslim women in Denmark wear full-face veils, according to researchers. Activists have denounced the government for infringing on women's right to choose how to dress. "Instead, the law criminalises women for their choice of clothing - making a mockery of the freedoms Denmark purports to uphold", Deputy Europe Director Fotis Filippou said in a statement.
In May, Denmark became the latest in a series of European nations to ban face veils in public, saying that it is a necessary measure to uphold the country's secular values.
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Even among the viable addresses, some include only a city name or are listed as "calle sin nombre", or "street without a name". Once a parent chooses to reunite with a child, the ACLU asked that the government reunite the family within seven days.