The Security Council also rejected another Russian-drafted resolution that would have welcomed an investigation by the Organisation for the Prohibition of Chemical Weapons (OPCW) of allegations of a weekend chemical attack in the suburbs of Syria's capital.
Syria's government and its ally Russian Federation have denied the chemical attack took place, but rescuers and medics said that dozens of people, including many women and children, were killed.
Twelve council members voted in favour, while Bolivia joined Russian Federation in voting against, and China abstained.
The United Nations Security Council rejected a Russian-drafted resolution Tuesday on investigating chemical weapons use in Syria after Moscow vetoed a competing US -proposed measure.
Sweden's ambassador, Olof Skoog, who tried unsuccessfully to find a compromise solution, told the council after the third vote that he was disappointed.
Russian Federation and the United States tangled on Tuesday at the U.N. Security Council over Syria as they blocked attempts by each other to set up worldwide investigations into chemical weapons attacks in the war-ravaged country.
After the defeat of Russia's second resolution, Russian ambassador Vassily Nebenzia said to USA ambassador Nikki Haley: "I would once again ask you, once again beseech you, to refrain from the plans that you're now developing for Syria". "There is nothing independent about that", she told the Security Council.
Last year, the United States launched missile strikes against a Syrian airbase from two navy destroyers after the Syrian Government was alleged to have used chemical weapons, leading to civilian fatalities.
In order to pass, a resolution needs nine votes in favour and no vetoes by the five permanent members: Russia, China, France, Britain or the United States.
It too failed to pass the threshold of nine. "This is very alarming for us", he said. The US, Britain and France voted against both measures but did not have to use their vetoes.
Tuesday's intensive voting came as Security Council members were striving to set up a mechanism to determine which side was accountable for the chemical weapons use in Syria.
The Syrian Foreign Ministry also said Syria will help the OPCW to investigate the alleged attack.