The council is now expected to vote Friday on the measure that would endorse a fresh UN initiative to restart talks.
The US-drafted text included a strong appeal to the Polisario Front to immediately withdraw from the Guerguerat strip, which has become a potential flashpoint between the independence fighters and Moroccan troops.
"The council wants to see if there is any significant development on the ground in these hours," said a council diplomat who asked not to be named.
"We heard that there might be some," he added, referring to the UN demand for the Polisario to withdraw.
The council is now expected to vote Friday on the measure that would endorse a fresh UN initiative to restart talks between Morocco and the Algeria-backed Polisario on settling the decades-old conflict.
France, which has friendly ties with Morocco, had insisted on a pullback from the Guerguerat post near the Mauritanian border after Morocco withdrew its forces in February.
"It is indeed time to look ahead and to relaunch negotiations, that is what we want," French Ambassador Francois Delattre told reporters on Tuesday.
"There is one issue we need to solve and that is Guerguerat," he said.
Morocco and the Polisario fought for control of Western Sahara from 1974 to 1991, when Rabat took over the desert territory before the signing of a UN-brokered ceasefire.
Rabat, which considers Western Sahara an integral part of Morocco, proposes autonomy for the resource-rich territory, but the Polisario Front insists on a UN referendum on independence.
The council diplomat said a withdrawal from the buffer strip would lead to changes in the resolution and pave the way to the appointment of a new UN peace envoy who would shepherd the talks.
The long-serving previous UN envoy, Christopher Ross, resigned last month after Morocco accused him of bias in favor of the Polisario.
Former German president Horst Kohler has been tipped to replace him.
The Polisario moved forces in Guerguerat last year in response to Morocco's decision to build a road in a zone it considers "liberated territory."