The two-page letter to Prime Minister Jean-Pierre Raffarin "threatens France with reprisal attacks following the 10 February adoption of the law banning the headscarf (hijab)," Le Parisien news director Christian de Villeneuve said.
On 10 February, France's lower house of parliament, the National Assembly, voted through the bill banning the wearing of conspicuous religious symbols in state schools. The Senate approved the measure on 3 March.
De Villeneuve said the letter was delivered to the newspaper's offices by ordinary mail, in a typed envelope addressed to him.
He gave it to the journalist dealing with "terrorism" issues, who then called police to verify the authenticity of the claim. Paris prosecutors quickly opened an inquiry into the matter.
"It is obviously not yet possible to assess the worth of this message"
interior ministry, France
The group calling itself calling the Movsar Barayev Commando, threatened both the national territory and French interests abroad, the interior ministry said.
"It is obviously not yet possible to assess the worth of this message," the ministry said in a statement.
The group's name appeared to be a reference to Movsar Barayev, who organised the Chechen commando raid and hostage-taking at a Moscow theatre in October 2002 that ended with 129 dead. He died in the special forces raid on the theatre.
The ministry said in a statement the letter was written "on behalf of the servants of Allah, the powerful and wise". Earlier statements had said that was the name of the hitherto unknown group.
Interior Minister Nicolas Sarkozy said that experts were "in the process of analysing" the threats.
Sources close to the investigation said the group was until now unknown to French intelligence services, who were in the process of researching the organisation.
Raffarin has called a meeting of parliamentary leaders on Thursday to discuss "terrorist risks" in France and the government's security plans.
Earlier on Tuesday, French President Jacques Chirac said after talks with German Chancellor Gerhard Schroeder: "France is not currently a specific target, but like all democracies, it is not immune from terrorist acts."