United Nations Secretary-General Antonio Guterres listens to members of the United Nations Security Council after voting against a Russian resolution condemning "aggression" against Syria by the U.S. and its allies during an emergency meeting on Syria at the U.N. headquarters in NY, U.S., April 14, 2018.
The threats of USA military action against Syria "should make us seriously anxious, all of us", Mr Nebenzia said.
Russian President Vladimir Putin called the operation an "act of aggression", and Iran said it was a "criminal" attack.
Russian Ambassador to the United Nations Vasily Nebenzya speaks after Members of the United Nations Security Council voted against a Russian resolution condemning "aggression" against Syria by the U.S. and its allies during an emergency meeting on Syria at the U.N. headquarters in NY, U.S., April 14, 2018.
The US push for a new inquiry came amid heightened tensions over possible US military action in Syria, with President Donald Trump saying that "major decisions" would be taken within 48 hours.
In a statement, Mrs May said: "The Syrian regime has a history of using chemical weapons against its own people in the most cruel and abhorrent way". Russia vetoed a US text, while two Russian-drafted resolutions failed to get a minimum nine votes to pass.
Ms Haley said the Russian draft would have allowed Russia to choose the investigators and assess the outcome of the investigation.
She said the United States "went the extra mile" to get Russian support for the resolution to ensure that a new investigative body would be impartial, independent and professional - provisions she said were not in the rival Russian resolution. He accused the United States, France and Britain of "demonstrating a blatant disregard for worldwide law".
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"You do not want to hear the fact that no traces of a chemical attack were found in Douma", Mr Nebenzia said.
Washington bombed a Syrian government air base previous year over a toxic gas attack.
He accused the U.S. of introducing the resolution knowing it would not pass so they could use it as a pretext to attack Syria.
Under the current draft resolution, UNIMI would be established for one year and work with the Organisation for the Prohibition of Chemical Weapons (OPCW) to identify perpetrators of the chemical attacks. It blamed Islamic State militants for mustard gas use.
Russian Federation proposed its own draft resolution in January to create a new investigation. The US, Britain and France voted against both measures but did not have to use their vetoes.
"Armed force under mendacious pretext against Syria, where, at the request of the legitimate government of a country, Russian troops have been deployed, could lead to grave repercussions", Nebenzia said.
Mr Nebenzia said two groups of OPCW experts could be on the ground "as early as this week".