"This is not a ban on religious clothing, this is a ban on masking," Jacob Ellemann-Jensen, spokesman for the Liberal Party, told reporters on Friday after his party, the largest in the coalition government, decided to back a ban.
This would effectively mean a ban on the niqab and the burqa, he added.
Around 200 women in Denmark wear such garments, according to researchers.
The three-party centre-right minority government, its ally the Danish People's Party and the main opposition Social Democrats have all said they are in favour of a ban, though they are still discussing how the ban should be designed and enforced.
"There will come a masking ban in Denmark. That's how it is," Foreign Minister Anders Samuelsen said on Facebook.
His party, the Liberal Alliance, had previously been one of the staunchest opponents of a ban, saying it limited people's ability to freely choose their attire, but has now aligned its stance with that of the other coalition parties, the Conservatives and the Liberals.
"So if it is practically possible to have such a ban without betraying ourselves or our own values, then the Liberal Alliance will vote for it," Samuelsen said.
The Social Democrats, Denmark's biggest party, has also signalled support in principle for a ban on garments such as the burqa, which it said oppressed women.
"We are ready to ban the burqa if that is what it takes ... But there are some dilemmas, not least with regards to how such a ban would be enforced," said the Social Democrats' leader Mette Fredriksen during a debate in parliament on Thursday.
Norway's government in June proposed a ban on face-covering Muslim veils in kindergartens, schools and universities.
