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The 15 nations on the council also said in a unanimously agreed statement that they "deplore" the rapidly deteriorating humanitarian situation in the country, where an 11-month government crackdown on pro-democracy protesters has left over 7500 civilians dead, according to the United Nations.
France's UN mission announced the agreement on the non-binding statement via its Twitter account (@franceonu).
It is the first statement on Syria from the council, which has been deadlocked on the issue for months, since August 2011, when it rebuked Damascus in a so-called "presidential statement" for the escalating violence there.
Since that time, Russia and China have twice vetoed Security Council resolutions condemning Damascus and calling for an end to the violence, saying Western and Arab nations are pushing for Libya-style "regime change" in Syria.