At the meeting, the fifth in a week on chemical weapons in Syria, Russia and its supporters again clashed with the U.S. and its allies over a suspected poison gas attack on April 7 in the Damascus suburb of Douma.
The Russia-drafted resolution won three votes at the Security Council, far below the nine votes required for adoption.
In a US military action a year ago in response to a sarin gas attack, the Pentagon said missiles took out almost 20 per cent of the Syrian air force.
On Sunday, Haley made clear the United States won't be pulling troops out of Syria right away, saying US involvement there "is not done".
France's defense minister said early Saturday that Russian Federation was warned ahead of the joint attacks on Syria, though Dunford said earlier in the evening that the only warning Russian Federation was given was "the normal deconfliction of the airspace - the procedures that are in place for all of our operations in Syria".
The Russian embassy in US wasted no time in reacting to the strikes late Friday in the USA, with Ambassador Anatoly Antonov saying on Twitter, "The worst apprehensions have come true".
The United States will want to maintain a dialogue with Russia about strategic stability following Western missile strikes on Syria, Russian news agencies cited a Russian Foreign Ministry official as saying on Sunday. Russian UN ambassador Vassily Nebenzia said after the vote. "The United States of America will not allow the Assad regime to continue using chemical weapons".
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Putin responded to Saturday's attack by calling the strikes "an act of aggression against a sovereign state that is at the forefront of the fight against terrorism".
"We are confident that we have crippled Syria's chemical weapons program".
This was stated by U.S. Ambassador to Russian Federation.
There were no immediate plans for more attacks, US Defence Secretary James Mattis said.
Ryabkov also said Russian Federation would study a United Nations resolution on Syria proposed by the US, France and Britain, but added that it would be hard to reach a compromise on the issue, TASS reported. Britain believes "that is wholly within the principles and practices of the United Nations", she said.
Worldwide investigators from the global chemical weapons watchdog are in Syria and were due to start their inquiry on Saturday into the suspected toxic gas attack.
The draft resolution will establish an independent investigation of allegations of chemical attacks in Syria with the aim of identifying the perpetrators. And it would establish a new body to determine responsibility for chemical attacks, call for a cease-fire in Syria, unimpeded access for all humanitarian aid, and an urgent resumption of negotiations on a political settlement.