UN Secretary General Ban Ki-moon said he hoped the intervention would help restore "Mali's constitutional order and territorial integrity".
Thousands of African troops are due to join Malian and French forces to help push back the rebels' offensive.
France intervened on Friday after the Islamists began advancing southwards.
French authorities said they had feared that the rebels would march on the capital, Bamako, creating a grave security threat for the wider region.
On Monday, the Security Council convened in New York for an emergency meeting at France's request.
After the meeting, France's UN ambassador Gerard Araud said his country had the "understanding and support" of the 14 other Security Council members.
But he added that France also wanted the deployment of a West African force to happen "as quickly as possible".
By Barbara PlettBBC UN correspondent
The Security Council's support for the French military intervention is an indication of the deep concern here about the growing strength and control of armed extremist groups in Mali.
Diplomats seem most preoccupied about how quickly African troops can get to the country to help Mali's weak army.
That's the UN plan, but the resolution authorising it envisaged a timeline over many months to prepare for an offensive, alongside a political reconciliation process between the government and nationalist rebels.
That's been disrupted by the Islamist advance and the French intervention. The plan is being fast-tracked now, with African contingents set to arrive in Bamako as early as next week.
Mr Araud said France wanted the Africans to take over the military operation as soon as possible, but he admitted it wasn't clear how this transfer was going to happen. The danger is that the Africans might not be able to take on the Islamists with the West playing only a supporting role,  sucking France into a long military engagement.
The force will be deployed under UN Security Council resolution 2085, which was passed in December and allows for a 3,000-strong African-led mission to intervene in Mali later this year in the absence of any negotiated solution.
The African troops are expected in Mali in "coming days and weeks", Mr Araud said, adding that the Nigerian commander of the force was already on the ground.
Mr Ban echoed Mr Araud's call for rapid deployment of an African force.
"The Secretary-General welcomes that bilateral partners are responding, at the request and with the consent of the government of Mali, to its call for assistance to counter the troubling push southward by armed and terrorist groups," his office said in a statement.
However the Islamist advance and French response also "underscore the urgency of implementing all aspects of the resolution".
France says its air strikes have forced back Islamists who took control of northern Mali last year, though the rebels seized one town on Monday.
French Foreign Minister Laurent Fabius said the West African force would include 600 troops from Nigeria, 500 each from Niger, Burkina Faso, Togo and Senegal, and 300 from Benin.
He said France's involvement would last "a matter of weeks".
France has sent about 550 troops to the central town of Mopti and to Bamako, and a defence ministry official told Reuters troop numbers would increase to 2,500 in coming days.
At least 11 Malian soldiers and a French helicopter pilot have died in Mali. More than 100 militants are reported to have been killed.
France's war in the desert
Aid workers said many people had been fleeing areas targeted by French air strikes over the past four days.
A spokesman for the International Committee of the Red Cross said the humanitarian situation was "fast deteriorating"
"Mass displacement of the population has already been observed, casualties have been reported and we're trying our best to address the humanitarian needs of the population," said Ali Naraghi.
France intensified its air strikes on rebel targets over the weekend, with its aircraft also bombing the town of Gao in eastern Mali. On Monday witnesses told AFP news agency that there had been air strikes on Douentza for a fourth consecutive day.
Mali a risk for 'new' Hollande
Residents in several northern towns also told AFP that Islamists in several key northern towns including Gao and Douentza had either fled or taken cover from the air strikes by Monday.
Rebels of the al-Qaeda-linked Movement for Oneness and Jihad in West Africa (Mujao), said that France would pay for its intervention.
Meanwhile, Algeria, which has allowed French jets to cross its airspace, said it had closed its long desert border with Mali.
Islamist groups and secular Tuareg rebels took advantage of chaos following a military coup to seize northern Mali in April 2012.
But the Islamists soon took control of the region's major towns, sidelining the Tuaregs.
One Islamist group, Ansar Dine, began pushing further south last week, seizing Konna.
The town has since been recaptured by Malian troops with French aerial support.
The UN Security Council has unanimously backed France's military intervention in Mali to fight Islamist rebels, officials have said.