French special forces were battling Islamist rebels in central Mali on Wednesday in the first major ground operation of the six-day offensive, DPA reported.
President Francois Hollande told the French parliament that he would seek the legislature's approval if the intervention lasted longer than four months.
French troops were fighting alongside the Malian Army against Islamist rebels in the town of Diabaly, about 400 kilometres north-east of the capital Bamako.
French broadcaster BFM TV quoted witnesses as describing violent clashes between the French and Malian forces on one side and the rebels, who seized the town on Monday.
Rebels have controlled the north of the country since March 2012 and began to push south last week, prompting France to launch a military intervention.
The International Criminal Court in The Hague, meanwhile, said it had opened an investigation into alleged war crimes in Mali since January 2012.
"The legal requirements have been met. We will investigate," said ICC prosecutor Fatou Bensouda. The crimes being investigated include murder, torture, extra-judicial executions and rape.
"Since the beginning of the armed conflict in January 2012, the people of northern Mali have been living in profound turmoil," Bensouda said. "At each stage during the conflict, different armed groups have caused havoc and human suffering through a range of alleged acts of extreme violence.
"I have determined that some of these deeds of brutality and destruction may constitute war crimes."
In south-eastern Algeria, Islamist gunmen who claim to be holding 41 foreign workers hostage at a gas facility have demanded an "immediate end" to the French intervention in Mali, according to a statement published by Mauritania's ANI news agency.
"We hold the Algerian and French governments and the (other) hostages' countries fully responsible for the delay in satisfying our demands, chief among which is the immediate end to the attack on our (people) in Mali," said an Islamist brigade affiliated to the al-Qaeda in Islamic Maghreb group.
Hollande has justified the intervention by saying that if France had not intervened, "Mali would have been fully conquered and the terrorists would be in position of force today."
Earlier Wednesday, when asked how long France would remain in Mali, Hollande said: "It will depend on what we are faced with. What we're facing is serious. These are people with extremely sophisticated material that they brought from Libya.
"We will stay as long as needed to defeat this offensive."
Asked whether he thought France would be out by summer, Hollande said: "I think so. We have no vocation to remain in Mali."
But it would be wrong to set an exit date at this stage, he said. "We will leave when we have achieved our objectives."
Until now, French forces have been supporting the Malian Army mainly through airstrikes against rebel positions. But the aerial campaign has failed to flush the rebels out of the centre of the country.
France has deployed 800 troops - a number that is set to be increased threefold. French media earlier said a few hundred soldiers and about 30 vehicles were en route to Diabaly.
In seizing Diabaly, the rebels opened up a second front in the fighting that had previously been centred on the town of Konna, about 700 kilometres north-east of Bamako.
The fall of Konna to the northern-based rebels last week triggered France's intervention.
West African troops will assist in the intervention. The United Nations last year approved the deployment of an African force.
Nigeria, which was to send 900 soldiers, is to lead the force. Benin, Ghana, Niger, Senegal, Burkina Faso and Togo have also pledged to take part.
Germany has offered two military transport planes for the African troops. Chancellor Angela Merkel said she and Hollande would discuss possible further support when they meet Tuesday to mark 50 years since both nations signed the Elysee Treaty.
"Depending on the situation, we will make a decision," Merkel said, adding that her government would not shy away from seeking a parliamentary mandate if a mission required it.
Merkel met with Ivory Coast President Alassane Ouattara, the current chair of regional bloc, the Economic Community of West African States, which is readying the deployment of a 3,300-strong force.
A European Union team is expected to arrive in Mali on or around Sunday, but military trainers will not follow until the rebel have been pushed back by French and African forces.
EU foreign ministers are to Thursday approve the launch of the training mission.
Kristalina Georgieva, the bloc's aid commissioner, expressed concerns to dpa Insight EU of a "protracted conflict that creates a massive refugee flow in the neighbouring countries," including Burkina Faso, Mauritania and Niger.
She said the EU was working with international partners on contingency plans in order to be "prepared for the worst."
Italy pledged to support France's mission logistically, and Spain was also considering sending a transport plane to back the military operations.
