"France pays the cost of its violence on Muslim countries and the violation of their sanctity," AQIM, the north African branch of the Al Qaeda, said in a statement published on jihadi websites, CNN reported.
France is reeling from an attack at the Charlie Hebdo satirical newspaper, which killed 12 people Wednesday, the death of a policewoman Thursday, and the siege of a Jewish supermarket Friday that left four hostages dead.
Three terrorists in the attacks were killed, but a suspected co-conspirator remains on the loose -- possibly in Syria.
The warning from AQIM comes just before Charlie Hebdo, known for its controversial depiction of the Prophet Mohammed, is set to publish again Tuesday. The issue will hit newsstands Wednesday.
This time, the cover features a drawing of a frowning Prophet Mohammed with a teardrop coming from his eye.
"All is Forgiven," the cover headline says in French.
In the prophet's hands, there is a sign that says "Je suis Charlie" or "I am Charlie."
From Paris to Jerusalem, Tuesday would mark a day of mourning for the victims in last week's attacks.
The bodies of four hostages killed in the Jewish store siege brought to Israel Tuesday morning. All four - Philippe Braham, Yohan Cohen, Yoav Hattab and François-Michel Saada - will be buried at the Govat Shaul cemetery in Jerusalem.
A Muslim policeman killed while trying to pursue the assailants from the Charlie Hebdo attack will be laid to rest Tuesday.
While France is grappling with a new wave of terrorism, concerns about future attacks have spilled well across its borders.
The US Department of Homeland Security (DHS) is boosting security at more government buildings across the country. But the exact locations are "law-enforcement sensitive", DHS Secretary Jeh Johnson said in a statement.
Johnson also noted that the Transportation Security Administration has ramped up the number of random searches of passengers and carry-on luggage at US airports.
The White House tried damage control Monday after widespread criticism that neither President Barack Obama nor any other high-ranking US official joined a massive anti-terrorism march in Paris that drew 40 other world leaders.
White House spokesperson Josh Earnest acknowledged "we should have sent someone with a higher profile", not even trying to justify the fact that the largely unknown US Ambassador to France, Jane Hartley, was the top American official at Sunday's rally.
While the US has not faced a physical terror attack since the incidents in France, Islamic State (IS) sympathisers did hack the Twitter account of the US Central Command.
A series of unusual tweets were published Monday with apparent warnings from the IS, as well as links, images and Pentagon documents that reveal contact information for members of the military.
The first tweet read: "AMERICAN SOLDIERS, WE ARE COMING, WATCH YOUR BACK. IS."
"CyberCaliphate" and "i love you isis" were sprawled out in white letters against a black screen at the top of the Twitter page.
The account was suspended, but defence officials say no classified information was obtained and no military networks were compromised.