Fighting has raged in Idlib and nearby areas in northwest Syria since government troops started pushing into the enclave on April 30, trying to retake the country's last rebel-held redoubt after eight years of civil war. The U.N. says an estimated 3 million people are caught in the crossfire.
"It was really simple," Kuwaiti Ambassador Mansour Al-Otaibi said when asked about the proposal at an unrelated news conference.
Russia's U.N. mission didn't immediately respond to an inquiry about the proposed statement.
The Security Council has struggled to speak with one voice on Syria in recent years. In one notable example, a 2017 Russian veto put an end to an initiative that determined accountability for chemical attacks in Syria. That effort was run jointly by the U.N. and the Organization for the Prohibition of Chemical Weapons.
At points, the U.S. has accused Russia, a close Syrian ally, of using its veto-wielding seat to stop the council from taking important steps to stanch the violence and suffering in Syria.
Russia, in turn, has said its critics are trying to score rhetorical points while it has made concrete efforts, such as joining with Turkey to broker an Idlib cease-fire in September.
Russia and Syria, which is not a council member, say Damascus is doing what is needed to fight terrorists.
In a recent sign of the council's divide on the issue, 11 council members, including Germany, Kuwait, Belgium and the U.S., issued a statement last month that also expressed concern about the intensifying hostilities around Idlib and the potential for humanitarian catastrophe. Four council members — Russia, China, South Africa and Indonesia — didn't join in supporting that statement.
Mansour, whose country holds the council's rotating presidency this month, said Monday that members would continue discussions.