PARIS, France (CNN) -- Al Qaeda threatened to "take revenge" on France "by every means and wherever we can reach them" because of a debate in France over whether the burqa, a traditional Islamic woman's covering, violates French law, according to a statement posted on radical Islamist Web sites.
A woman wears traditionnal Muslim dress in Venissieux, near Lyon, France.
"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]."
The statement is dated June 28, five days after French President Nicolas Sarkozy controversially told lawmakers that the traditional Muslim garment was "not welcome" in France.
A day later, the French National Assembly announced the creation of an inquiry into whether women in France should be allowed to wear the garment.
A cross-party panel of 32 lawmakers will investigate whether the burqa poses a threat to the secular nature of the French constitution. They are due to report back with their recommendations in six months.
The al Qaeda statement accused France of "organizing its ranks to fight a new blatant war against our sisters wearing the burqa."
CNN cannot verify the authenticity of the statement, which also accused the French of "committing all of these grievances in a time when we see their women flooding our nations, filling our shores, poorly dressed and nude in a deliberate defiance to the feelings of Muslims and in clear contempt to the teachings of the Islamic faith, traditions and norms."
"Our Muslim brothers in France in particular and in Europe in general are increasingly troubled by the practices of the French politicians and their leaders, and their constant harassments of our people regarding the burqa issue," said the statement.
"Yesterday they targeted the veil, today the burqa and maybe tomorrow their evil hands could be extended to defame our pillars of faith, like praying, fasting or the pilgrimage," it added.
Sarkozy made the statement last week, in an address to parliament.
"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.
The right of Muslim women to cover themselves is fiercely debated in France, which has a significant Muslim minority but also a staunchly secular constitution.
In 2004, the French parliament passed legislation banning Muslim girls from wearing head scarves 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.
Last year, France's top court denied a Moroccan woman's naturalization request on the grounds that she wore a burqa.
Between 5 and 10 percent of France's population of 64 million is Muslim, according to CIA estimates. The country does not collect its own statistics on religion in accordance with laws enshrining France's status as a secular state.
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.