Paris, France (CNN) -- French lawmakers could recommend Tuesday that the fiercely secular country ban the burqa, the full-body covering worn by some Muslim women.

French President Nicolas Sarkozy controversially told lawmakers in June that the traditional Muslim garment was "not welcome" in France.

"The problem of the burqa is not a religious problem. This is an issue of a woman's freedom and dignity. This is not a religious symbol. It is a sign of subservience; it is a sign of lowering. I want to say solemnly, the burqa is not welcome in France," Sarkozy said.

A day later, the French National Assembly announced the creation of an inquiry into whether women in France should be allowed to wear the covering.

A cross-party panel of 32 lawmakers has been studying whether the burqa poses a threat to France's constitutionally-mandated secularism. A ban could make it impossible for women who wear the burqa to receive any public services, from buying a bus ticket to picking up a child at school.

Some members of parliament want to go even further with a law that might make wearing a full veil subject to a $1,000 fine.

"You know, it is not only an article of clothing to hide your face," said parliamentary majority leader Jean-Francois Cope. "I am sorry, it's a choice which is not compatible with the rules of the republic."

Within days of Sarkozy's announcement, al Qaeda threatened to "take revenge" on France "by every means and wherever we can reach them," according to a statement posted on radical Islamist Web sites.

Connect the World: Is it right to ban the burqa?

"We will not tolerate such provocations and injustices, and we will take our revenge from France," said the statement, signed by Abu Musab Abdul Wadud, calling himself "commander of al Qaeda in North Africa [Islamic Maghreb]."

But more than half of French people support the ban, according to a recent opinion poll. The Ipsos poll for Le Point magazine found 57 percent of French people said it should be illegal to appear in public wearing clothes that cover the face, like the burqa.

That's despite government estimates that less than 2,000 women in the country actually wear the full Islamic veil.

France has about 3.5 million Muslims, representing about 6 percent of the population, according to research by the Pew Forum on Religion & Public Life. The country does not collect its own statistics on religion in accordance with laws enshrining France's status as a secular state.

French lawmakers believe the burqa is a growing phenomenon beneath which lies a not-so-subtle message of fundamentalism.

Those who advocate the ban say women are often forced to wear full veils by the men around them -- husbands, fathers or brothers -- and that it is a sign of subjugation.

However, women who actually wear the veils deny that.

"You are going to isolate these women and then you can't say that it is Islam that has denied them freedom, but that the law has," said Mabrouka Boujnah, a language teacher of Tunisian origin.

Boujnah, who at 28 is about to have her first child, says she came to wearing a full veil gradually, after wearing headscarves as an teenager. She believes a law like the one being discussed will take away fundamental rights of Muslim women.

She and her friend Oumkheyr say they prefer to cover their faces out of piety.

Oumkheyr, in her 40s and unmarried, says she even has friends who wear full veils against the wishes of their husbands. Oumkheyr, who is from Algeria, would not give her last name.

The women, both French citizens, say they are only following their religious beliefs and France should respect that.

But even some Muslims here think the full veil goes too far.

There is nothing in Quran that directs women to cover their faces, said Imam Hassen Chalghoumi, who runs the Islamic center in Drancy, a Paris suburb. He said it is ridiculous to do so in France.

While French lawmakers from both left- and right-wing parties seem ready to pass at least a resolution discouraging the full veil in public places, it's a choice Boujnah and Oumkheyr say they will continue to make. They pair say they will willingly show their faces for identification purposes -- but if it comes to it, they will break any law that runs contrary to their religious beliefs..

At the very least any law directed at full veils is likely to be challenged in the courts both here and at the European level. What's more, even police find it hard to imagine how they could -- or would -- enforce such a ban.

In 2004, the French parliament passed legislation banning Muslim girls from wearing headscarves in state schools, prompting widespread Muslim protests. The law also banned other conspicuous religious symbols including Sikh turbans, large Christian crucifixes and Jewish skull caps.

In 2008, France's top court denied a Moroccan woman's naturalization request on the grounds that she wore a burqa.

France is not the only European Union country to consider banning the burqa. Dutch lawmakers voted in favor of a ban in 2005, although the government at the time left office before legislation could be passed.

--CNN's Jim Bittermann in Paris contributed to this report.