"France has attacked Islam. We will strike at the heart of France," said a leader of the Movement for Oneness and Jihad in West Africa – an offshoot of al-Qaeda in the Islamic Maghreb – on Monday.
Asked where they would strike, Abou Dardar responded to Agence France-Presse: "Everywhere. In Bamako, in Africa and in Europe."
Authorities in France were already on high alert over fears of a backlash on home soil by extremists.
The movement's official also referred to France's eight hostages held in the Sahel region.
"We will make a statement on the hostages today. From today all the mujahideen are together."
The French offensive has blocked the advance of extremist forces towards the capital Bamako from their bases in the north which they have controlled since last April.
Fighter plane attacks
On Sunday French Rafale fighter planes struck bases used by al-Qaeda-linked fighters in Gao, the main city in north Mali, and Kidal.
Sixty extremist were killed in Gao alone on Sunday, according to residents and a regional security force.
French warplanes also attacked rebel stockpiles of munitions and fuel further north at Afhabo, 50 kilometres from Kidal, a regional security source said. The area is a stronghold of Ansar Dine.
And they hit a base further east at Léré, near the border with Mauritania, according to witnesses and a statement from Doctors Without Borders.
Algeria on Sunday granted France permission to fly through its airspace to reach its targets. Previously, Algiers was hostile to any foreign intervention in Mali.
France launched the operation alongside the Malian army on Friday to counter a push south by the insurgents who had threatened to advance on the capital Bamako.
Gao residents said earlier that the French airstrikes had levelled the extremists' position and forced them to flee.
"We can see smoke billowing from the base. There isn't a single Islamist left in town. They have all fled," a teacher said, speaking on condition of anonymity.
Hollande's cabinet meeting
Residents of Timbuktu, said they were eager for French jets to arrive.
Everyone agrees, said one resident, even if there was a risk that civilians might be killed in such an action. Already there was growing panic among the extremists there, he added.
French President Francois Hollande was to hold a Cabinet meeting devoted to the Mali crisis early on Monday.
And at the request of Paris, the UN Security Council was to meet later on Monday to discuss the conflict, a spokesperson for France's UN mission said.
Aides to Hollande described the militants as better trained and armed than expected.
"What has struck us markedly is how modern their equipment is and their ability to use it," one said, referring to the rebels' hit on a French helicopter, which fatally wounded its pilot, France's only confirmed loss.
African intervention force
Meanwhile a west African intervention force for Mali was taking shape.
The force has been authorised by the UN Security Council to help the Malian government reclaim control of the north. It will be commanded by General Shehu Abdulkadir of Nigeria, which will provide around 600 men.
Burkina Faso, Niger, Senegal and Togo all pledged around 500 troops this weekend, while Benin said it would send 300. It remained unclear however when these forces would arrive.
Media reports have said France is deploying about 500 troops in Mali.
The French mission will be at full-strength by Monday; primarily deployed around Bamako to protect the 6 000-strong expatriate community, said its commander, Colonel Paul Geze.
France's intervention has been backed by the European Union and the United States, while Britain is providing logistical support in the form of transport planes. – Sapa-AFP