The Council rejected a third text also proposed by Russian Federation which concerned the work of the fact-finding mission of the Organisation for the Prohibition of Chemical Weapons (OPCW), the implementing body of the Chemical Weapons Convention (CWC), which entered into force in 1997.
Russian Foreign Minister Sergei Lavrov said a reported chemical attack in Syria was staged by foreign agents.
The measure would instruct the Organisation for the Prohibition of Chemical Weapons (OPCW) to report within 30 days on whether Syria has fully disclosed its chemical weapons stockpile.
For eight years, the people of Syria have lived through a litany of horrors: atrocity crimes, sieges, starvation, indiscriminate attacks against civilians and civilian infrastructure, the use of chemical weapons, forced displacement, sexual violence, torture, detention and enforced disappearances, he said.
Voting for the resolution "would be like watching a fire and identifying that there is a fire", said Karen Pierce, Britain's United Nations envoy.
The White House said "no final decision has been made" on Syria after Mr Trump met his national security team.
Following air strikes launched at Syria by a US-led coalition including France and the UK as a response to a purported chemical weapons attack on civilians by forces loyal to Assad, United Nations Secretary-General António Guterres has warned that further aggressive moves by the West risk a "full-blown military escalation" in the region, according to the Independent.More news: Spending tax refunds, many have few options
U.S. Defense Secretary Jim Mattis told Congress that the Pentagon is still trying to pin down evidence related to the Douma attack, but French President Emmanuel Macron asserted that "we have proof " that "chemical weapons.at least chlorine" was used by the Syrian government in Douma.
Further actions violating the United Nations charter such as the recent US -led strikes on Syria will result in chaos in global relations, Russian President Vladimir Putin told his Iranian counterpart Hassan Ruhani over phone on Sunday.
Mr Trump has since tempered his remarks on attacking Syria and even as he consulted allies Britain and France, there were signs of efforts to prevent the crisis from spiralling out of control. A suspected chemical attack outside the Syrian capital of Damascus reportedly left more than 40 people dead.
By "deciding once again to use chemical weapons" in the rebel-held town of Douma, "the regime has reached a point of no-return", Delattre said.
Lavrov spoke to reporters in Moscow on Friday.
"Intelligence agencies of a state that is now striving to spearhead a Russophobic campaign were involved in that fabrication", he said.