The move heightened diplomatic tensions ahead of a key Russia-US-UN meeting in Geneva on Friday on organizing an international Syria peace conference.
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Russian diplomats refused to allow any mention in the statement of President Bashar Assad's tactics, diplomats said.
In the face of the obstacles, the United States decided to withdraw the draft which needs the approval of all 15 Security Council members to be released. A spokesperson said the US administration was "very disappointed" at the Russian blocking.
The United States wanted the statement to express "outrage at the use of air strikes by the Syrian government, in particular the use of heavy indiscriminate weapons, including Scud missiles and 'barrel bombs,' which were dropped on Aleppo" this week.
The Doctors Without Borders group says at least 189 people have been killed and nearly 900 wounded in the Aleppo bombings since Sunday.
The statement would have expressed concern at the general "escalating level of violence in the Syrian conflict and condemned all violence by all parties."
Russia would not comment publicly on the statement. But it has strongly defended Assad from Security Council action during the 33-month-old war in which the UN says well over 100,000 people have been killed.
"We are very disappointed that a Security Council statement expressing our collective outrage at the brutal and indiscriminant tactics employed by the Syrian regime against civilians has been blocked," said Kurtis Cooper, deputy spokesperson for the US mission to the United Nations.
"These barrel bombs - and the explosive materials contained within them - further underscore the brutality of the Assad regime and the lengths they will go to attack and kill their own people," he added.
"Regime air raids in and around Aleppo have continued unabated. Surely, at a minimum, the Security Council should be able to condemn such barbarities," said Cooper.
Russia and China have vetoed three UN Security Council resolutions proposed by western nations to increase pressure on Assad. Statements, which are not legally binding, have only rarely been agreed on Syria.
But Russia and the United States have jointly pressed for a peace conference that UN leader Ban Ki-moon wants to hold in Switzerland from January 22.
UN-Arab League peace envoy Lakhdar Brahimi will meet with Russian deputy foreign ministers Mikhail Bogdanov and Gennady Gatilov and US Undersecretary of State Wendy Sherman in Geneva on Friday to step up conference preparations.
The three sides have still to hammer out whether Iran and Saudi Arabia will be officially invited to the conference and other key details.
Iran, is a major backer of Assad, while Saudi Arabia supports the Syrian opposition. Iran's presence is controversial as it has not accepted a declaration adopted by the major powers in June last year which called for a transitional government in Syria.
The Syrian opposition does not accept Assad's presence in any interim government while the president has several times insisted that he will not stand down.
After the UN-US-Russia meeting, Brahimi will call wider talks with envoys from the United States, Russia, China, Britain, France, Iraq, Lebanon, Jordan, Turkey, the European Union and Arab League, said UN deputy spokesperson Farhan Haq.
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