It came amid reports the Al-Qaeda linked militants were abandoning some of their positions and converging on the mountainous region of Kidal, their northernmost bastion, 1,500 kilometres from the Malian capital Bamako and near the border with Algeria.
"The deployment towards the north... which began 24 hours ago, is on course with troops inside the towns of Niono and Sevare," French army spokesman Lieutenant Colonel Emmanuel Dosseur told reporters.
Niono is about 350 kilometres north-east of the Malian capital and 60 kilometres south of Diabaly, which was seized nearly a week ago by Islamists and then heavily bombed by French planes.
Sevare, 630 kilometres north-east of Bamako, has a strategically important airport. The town is also near Konna, whose seizure by Islamists on January 10 sparked the French military intervention in the former colony against the forces occupying northern Mali for about nine months.
However, there are conflicting reports about who is in control of Diabaly.
"In Diabaly, the situation is not very clear but it appears the rebel fighters have left the town," A French lieutenant-colonel, identifying himself as only Frederic, told news agency AFP.
On Sunday, French Foreign Minister Laurent Fabius said Russia had offered to help transport troops and supplies to Mali, and Canada had offered help to bring African troops to the country.
"There is transportation that will be partly by the Africans themselves, partly by the Europeans and partly by the Canadians…and the Russians have proposed to provide means of transport for the French, so it's fairly diverse," Fabius told radio station Europe 1.
Only about 100 soldiers from a planned 5,800- strong African force have so far reached Mali, while France said it has 2,000 soldiers already on the ground.
The announcement came a day after an emergency West African summit of the ECOWAS regional bloc called on the United Nations "to immediately provide financial and logistical backing for the deployment of MISMA", the African force.
Fabius, who also attended the summit, said it was time for the Africans to take charge of the task of halting the extremist advance "as soon as possible".
"It is vital that the maximum number of countries worldwide contribute" to the effort, Fabius said, speaking ahead of a donors' conference in the Ethiopian capital Addis Ababa on January 29.
Germany Foreign Minister Guido Westerwelle on Sunday responded to the appeal, pledging extra aid at the meeting but without setting an amount.
"The African troops need financial aid. During the donors' conference in Addis Ababa at the end of the month, Germany will assume its responsibilities," he wrote in the Sunday paper Bild am Sonntag.