"In this matter the government is taking a path it knows to be difficult, but a path it knows to be just," President Nicolas Sarkozy told the assembled ministers on Wednesday.
While Sarkozy's right-wing majority is expected to be able to push the law through parliament, constitutional experts have warned that it could be thrown out by judges and might fall foul of European law.
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"We are an old nation united around a certain idea of human dignity, and in particular of a woman's dignity, around a certain idea of how to live together," Sarkozy insisted.
"The full veil that hides the face completely harms those values, which are so fundamental to us, so essential to the republican compact."
According to the text of the law, no-one in France will be allowed to wear a garment "designed to hide the face". Those who flout it will be fined 150 euros (180 dollars) or sent on a course to learn the values of French citizenship.
Anyone who forces someone through threats, violence or misuse of a position of authority to cover her face because of her sex will be jailed for a year and fined 15,000 euros, the law says.
The law defines public spaces broadly to include all thoroughfares, all premises open to the public, such as shops, cinemas, restaurants and markets, and all government buildings.
France's highest administrative legal body, the Council of State, had warned the government that it might be legally impossible to impose and enforce such a ban, but Sarkozy and his supporters are determined to press on.
Some opposition Socialists have declared they will vote against a ban they feel will be impossible to enforce, and many Muslim groups oppose a ban they fear will stigmatise their religion.
Amnesty International appealed to French parliamentarians to "reject" the law.
A complete ban would "violate the right to freedom of expression and religion of those women who wear the burqa or niqab in public as an expression of their identity or their beliefs," the organisation said in a statement.
Opponents of the ban point to official figures that estimate that only 2,000 members of France's approximately five-million-strong Muslim population wear the niqab, or full-face veil.
