Hollande, making his first speech to the UN General Assembly, said Mali needs help to seize back territory from Islamist rebels, who captured the north and east of the country after a coup created a power vacuum in March.
"We have to act, act together and act quickly, because it is urgently needed," Hollande said, urging world leaders to back a UN Security Council resolution "to help Mali win back its territorial integrity."
Hollande said the situation in the north of the country is "is unbearable and unacceptable."
Human Rights Watch said on Tuesday that Mali's Islamist rebels are carrying out increasingly grave abuses in their pursuit of strict Islamic law.
The militias have arrested unveiled women, stoned an unmarried couple to death, publicly flogged smokers, amputated limbs of suspected thieves, and enlisted child soldiers as young as 12, the rights group said.
Hollande reiterated that Paris was prepared to support any initiatives taken by African nations to confront the crisis.
Mali has sent a letter to the United Nations formally seeking authorization for a West African-led military force, which French Foreign Minister Laurent Fabius has said would number about 3,000 troops.
UN chief Ban Ki-moon has convened talks on the crisis in the Sahel region on Wednesday on the sidelines of the UN meeting, due to be addressed by Hollande and US Secretary of State Hillary Clinton.
"The Malian government wants this force," Fabius said earlier, adding that the letter was signed by Mali's President Dioncounda Traore and Prime Minister Cheikh Modibo Diarra and had been sent to Ban on September 18th.
During a dinner late Monday, Hollande and Ban also discussed the possibility of appointing a UN envoy to Mali.
Chaos erupted in Mali in March when military putschists seized power in the capital, ousting President Amadou Toumani Toure, only to see the north and east fall to Tuareg rebels and Islamist militias.
HRW said there was little difference between the three main groups that capitalized on the power vacuum to seize the vast desert north, one of which is Al-Qaeda's north African branch, Al-Qaeda in the Islamic Maghreb (AQIM).
France has offered to supply logistical support for any military force, in what is a delicate situation for the former colonial power, with six French hostages held in the area by AQIM.
The group threatened last week to execute hostages if there is any military intervention in the region.
"The need to free our hostages should not cause us to abandon efforts to ensure Mali's territorial integrity," Hollande said.
"Let it be understood that there is no question of deploying French troops on the ground," Fabius stressed earlier, denying French press reports which suggested French special forces are already in Mali.
"It is up to the Africans, working under a UN mandate, to take the necessary action," he said, adding France wanted to act as a facilitator to help Mali rid itself of terror groups.
However, there are still hurdles to overcome including defining the objectives of any forces and the terms of an agreement between the Mali government and the Economic Community of West African States (ECOWAS).
ECOWAS has 3,300 regional troops on standby but wants UN approval and has been awaiting the go-ahead from Mali.
Mali will only accept troops from ECOWAS as part of the intervention, a source close to the Malian president's office said Tuesday, adding that the mission would last for six months, renewable if Mali deemed it necessary.