The council has been calling on the Ecowas group of west African nations and the African Union (AU) to provide details of a plan to intervene.
But only a few neighbouring countries have committed themselves to participate in the force, which could have 3,000 personnel eventually.
A military coup toppled president Amadou Toulani Touré in March and was swiftly followed by the north and east falling under the control of Tuareg separatists and armed Islamists linked to Al-Qaeda.
Friday’s resolution, which was passed unanimously, calls on Secretary-General Ban Ki-moon to work with Ecowas and the AU to submit “detailed and actionable recommendations” within 45 days.
The first draft’s 30-day deadline was considered unrealistic.
Once the details have been submitted to the Security Council, a second resolution will have to be passed to support deployment and that is not expected to happen before the end of 2012.
The UN is to provide “military and security planners” to help the preparations, while Hollande has promised logistical support from France. The US, which welcomed the Security Council decision, is also expected to give logistical support.
The European Union is to send 150 military trainers to Mali soon. EU foreign ministers will discuss the question at a meeting in Luxembourg on Monday.
The resolution also condemns human rights abuses in the north and "calls upon Malian rebel groups to cut off all ties to terrorist organisations," especially Al-Qaeda in the Islamic Maghreb.
It urges the transitional authorities in Bamako to speed up efforts to restore "constitutional order", while supporting the “sovereignty, unity and territorial integrity of Mali”.
A meeting is set for 19 October 19 in Bamako with representatives from Ecowas, the AU, the EU and the UN in an attempt to develop a "coherent strategy," a diplomat told the AFP news agency.