Following an African Union request for UN backing, France presented a draft resolution on Tuesday to back a decision by Africa's G5 - Burkina Faso, Chad, Mali, Mauritania and Niger - to set up a 5,000-strong counter-terrorism force in the Sahel region.
It would give a UN mandate to the G5 troops to "use all necessary means" to "combat terrorism, drug trafficking and trafficking in persons."
The United States had said the mandate lacked precision and that a council statement instead of a full-fledged resolution would provide sufficient support.
A revised draft resolution circulated to the Security Council on Friday specified that the armed groups to be targeted by the five-nation force are on the UN terror list.
UN Secretary General Antonio Guterres would be asked to report to the council on ways to support the force logistically and financially.
The European Union has already agreed to give 50 million euros to the regional force but the United States and Britain are unwilling to commit UN funds for the operation, diplomats said.
"The real issue is money," a Security Council diplomat said, asking not to be named.
A vote on the draft resolution may take place next week.
France sent troops to Mali in 2013 to fight jihadists and Tuareg separatists who had seized much of the north.
Although a peace deal has been reached with the Tuareg groups and the jihadists driven out of major cities, attacks on civilians and UN forces continue.
Three UN soldiers were killed and eight wounded in an attack in Kidal in the north of the country on Friday.
The Group to Support Islam and Muslims, a fusion of three Malian jihadist groups with previous Al-Qaeda links, claimed responsibility for the attack.