A call by German conservatives for a partial ban on the burqa - which covers the face and the body - is dividing the governing coalition.
The interior minister, Thomas de Maiziere, said conservative regional interior ministers had agreed on the move as part of security measures.
But the justice minister, Heiko Maas, has said the burqa and security should be kept separate.
The proposal, which would stop anyone wearing the veil in schools, universities, nurseries, public offices or while driving, requires parliamentary approval to become law.
Chancellor Angela Merkel's governing coalition has been divided over the issue after several attacks in Germany claimed by Islamic State, and amid record numbers of Muslim asylum seekers.
"We reject the full veil - not just the burka but the other forms of full veil where only the eyes are visible," Mr de Maiziere said.
"It doesn't fit in with our open society. Showing the face is a constituent element for our communication, the way we live, our social cohesion. That is why we call on everyone to show their face."
He added: "Whoever wants to work in public service cannot do so while wearing the full veil."
There are no official statistics on the number of women wearing the burka in Germany but Aiman Mazyek, leader of its Central Council of Muslims, is reported as saying hardly any women wear it.
In 2009, Spiegel magazine reported on a study by the Federal Office for Migration and Refugees which found that only one-third of Muslim women in Germany wore a headscarf.
Europe tussles over veil
Countries across Europe have wrestled with the issue of the Muslim veil - in various forms such as the body-covering burka and the niqab, which covers the face apart from the eyes.
The debate covers religious freedom, female equality, secular traditions and fears of terrorism.
The veil issue is also part of a wider debate about multiculturalism in Europe, as many politicians argue for a greater effort to assimilate ethnic and religious minorities.
France was the first European country to ban the full-face Islamic veil in public places.
The country has the largest Muslim minority in western Europe - about five million people - but it is thought only about 2000 women wear full veils.
Under the ban, which took effect in April 2011, no woman, French or foreign, is able to leave their home with their face hidden behind a veil without running the risk of a fine.
The penalty is a €150 fine and instruction in citizenship. Anyone found forcing a woman to cover her face risks a €30,000 fine.
The European Court of Human Rights upheld the ban in 2014 after a case was brought by a young French woman who argued that it violated her freedom of religion and expression.
Most of the population - including most Muslims - agree with the government when it describes the face-covering veil as an affront to society's values.
Critics - chiefly outside France - say it is a violation of individual liberties.
Women at French universities can wear headscarves but a ban on headcoverings and other "conspicuous" religious symbols at state schools was introduced in 2004.
It received overwhelming political and public support in a country where the separation of state and religion is enshrined in law.