French president François Hollande spoke to Malian president Ibarahim Boubakar by telephone on Monday.
Although Malian, French and UN military forces are deployed in the country, the desert town of Kidal remains the scene of anti-government protests.
The fighting on Saturday occured during Prime Minister Moussa Mara's visit to Kidal and claimed the lives of eight soldiers and 36 insurgents.
30 people - amongst them top civil servants, the regional director of Kidal, a prefect and the governor's adviser - are now being held hostage by the Tuareg separatist National Movement for the Liberation of Azawad (MNLA).
Mali sent troops on Monday to reinforce its presence in the rebel town, 1,500 km northeast of the capital, Bamako.
"We are mobilising the resources to fight this war" said Malian Prime Minister Moussa Mara, this as President Ibrahima Boubacar Keita is expected to raise the crisis in a TV address.
A French led military operation - in January 2013 - ousted the extremists, but sporadic attacks continue and Tuareg rebels demand for autonomy is not solved.