But Muslim leaders fear it will stoke tensions by stigmatising France's estimated five to six million Muslims, the biggest Islamic community in Europe.
The National Assembly lower house will hold a vote on the ban on July 13 and if passed it will then go to the senate in September.
AFP, the French news agency, said that only three deputies from the Green party have said that they will vote against the bill and that the main Socialist opposition had decided to boycott the vote
Martine Aubry, the Socialist party leader, told deputies at a meeting that while they should not vote against the bill, they should not take part in next week's vote, a Socialist party official told AFP.
"We are against the burqa but we believe that the means chosen to outlaw it are not good," said the party official.
The proposed law would make it illegal to cover the face anywhere in public and those caught wearing a full veil would face fines of $190 or be ordered to enrol in a "citizenship course".
Men who force their wives or daughters to wear the full veil face a fine of up to $37,754 and a one-year jail term, according to the draft legislation.
Nicolas Sarkozy, the French president, said earlier this year that the full veil, such as the niqab or the burqa, "hurts the dignity of women and is not acceptable in French society".
Many feminists from France's poor, multi-ethnic suburbs have spoken out in support of a ban, saying it could help young women who did not want to wear the veil but are forced to do so by their families.
According to public polls most French voters back a ban, but legal experts have warned that it could violate the constitution.
They have warned that the broad scope of the law banning the veil in all public places instead of just in state institutions could be struck down by the constitutional court.
Francois Fillon, the French prime minister, attempted to defend the move last week by inaugurating a mosque in a Paris suburb, drinking mint tea and eating dates with Muslim leaders.
Fillon said Muslims who wear face coverings were "hijacking Islam" by providing a "dark and sectarian image" of the religion that is "the opposite of the French Islam that you have contributed to build".
Fewer than 2,000 women wear the full-face veil in France, according to the interior ministry.
French politicians have said the law will also apply to tourists from the Middle East and the Gulf who are often seen fully veiled in luxury shops on the Paris boulevards.
Similar laws are pending in Belgium and Spain.