France is maintaining "very great vigilance" toward actions and statements by al Qaeda in the Islamic Maghreb, or North Africa, French Foreign Ministry spokesman Eric Chevallier said in a briefing.
"French authorities reaffirm their determination to fight terrorism," he added.
The Algeria-based group issued a statement on Islamic Web sites vowing to "seek vengeance against France" over Sarkozy's comments about face-covering Muslim veils such as the burqa and niqab. The declaration could not be independently verified.
Sarkozy said last weekand would turn women into prisoners. France's parliament created a commission to study the issue, which could lead to banning the Muslim robes from being worn in public.
Human Rights Watch said the move would be counterproductive, and a top British Muslim group said Sarkozy's comments were patronizing and offensive. Lebanon's most influential Shiite cleric called on the French leader to reconsider his statement.
The al Qaeda declaration called on followers to act "for the honor of our daughters and our sisters" and called on all Muslims "to respond to this hate."
Hard-line Algerian militants left over from a civil war between radical Islamists and government forces in the 1990s joined al Qaeda in 2006. They regularly target Algerian government forces and have tried to step up attacks against foreigners.