However, President Francois Hollande said France would only act under UN authorization.
Francois Hollande was responding to a plea by Malian President Dioncounda Traore for help to counter a renewed rebel offensive.
Earlier, an emergency meeting of the UN Security Council called for the rapid deployment of an African-led international force to Mali.
Armed groups, some linked to al-Qaeda, took control of northern Mali in April 2012.
They have enforced an extreme interpretation of Islamic law.
Analysts say Western nations are concerned that Mali’s north could become a base for terrorists to plan and launch international attacks.
The UN has approved plans to send some 3,000 African troops to Mali to recapture the north but they are not due to arrive until September.
“They (rebels) are trying to deliver a fatal blow to the very existence of this country,” Francois Hollande said.
“France, like its African partners, cannot accept this. I have decided that France will respond, alongside our African partners, to the request from the Malian authorities.
“We will do it strictly within the framework of the United Nations Security Council resolution. We will be ready to stop the terrorists’ offensive if it continues.”
Diplomatic sources said Francois Hollande and Dioncounda Traore would meet for talks in Paris next Wednesday.
It is not clear what form French intervention might take, but one possibility is the use of air strikes if the rebels advance on the strategic central town of Mopti.
Speaking shortly before Francois Hollande’s address, French War Veterans Minister Kader Arif appeared to rule out a speedy deployment of French troops to Mali.
“There is clearly an emergency but… there’s no point in rushing in,” said Kader Arif.
“At the same time, there can be no kind of engagement that could take place in this emergency without taking account of the international scale.”
Earlier this week, the militant Islamist group Ansar Dine said it had entered the key central town of Konna and intended to advance further south.
The army has refused to comment on the claim.
Following its emergency meeting on Mali on Thursday, the UN Security Council called for a “rapid deployment” of the African force and expressed “grave concern” at the capture of Konna by “terrorists and extremist groups”.
UN diplomats in New York said President Dioncounda Traore had appealed for help to Paris and to UN chief Ban Ki-moon.
“It basically said <<Help, France>>,” the US ambassador to the UN Susan Rice told reporters in describing the letter.
France was the colonial power in Mali until 1960.
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