The two veto powers said the Security Council measure, which supports an Arab League peace plan, violates Syria's sovereignty, The New York Times reported. The other 13 members of the council voted for the resolution.
Syrian dissidents said Saturday more than 260 people had been killed in the bombardment of Homs that began Friday night. While the stories filtering out of the city could not be confirmed, the attack would be the deadliest of the 11-month struggle between opposition protesters and the government of President Bashar Assad if they are true.
U.S. President Barack Obama issued a statement pointing out the attack on Homs occurred on the 30th anniversary of the massacre in Hama, carried out by Assad's father.
"The Syrian regime's policy of maintaining power by terrorizing its people only indicates its inherent weakness and inevitable collapse," Obama said. "Assad has no right to lead Syria, and has lost all legitimacy with his people and the international community."
The Syrian National Council said hundreds were wounded in the assault, which lasted from about 9 p.m. Friday to 1 a.m. Saturday, the Times reported. Activists said the military blocked roads, preventing the injured from getting to hospitals.
The council accused government forces of "randomly bombing residential areas," with women and children among those killed. Activists said most of the deaths occurred in the residential area of Khalidiya, where reports said a hospital was also destroyed, the BBC said.
"The Syrian National Council calls on everyone around the world to speak up and do something to stop the bloodshed of innocent Syrians," the council said in a statement.
Omar Shakir, a dissident in Homs, told The Washington Post many of those who died were in buildings that collapsed under missile attack from government forces surrounding Homs.
The Times said the assault apparently began after defectors attacked two military checkpoints and kidnapped soldiers.
Assad's government denied the toll, accusing activists of mounting a propaganda campaign before the Security Council vote.
Meanwhile, activists attacked Syrian embassies in Berlin, London and Cairo.
Andrew Tabler of the Washington Institute for Near East Policy said the government may have been heartened by Russian "stalling" on a U.N. Security Council resolution condemning Syrian government violence against dissenters.
Syrians in the United States and Britain said they had been in touch with friends and family in Homs who confirmed Shakir's account.
Dima Moussa, who was born in Homs and now lives in the United States, is a member of the Syrian National Council.
"At least four buildings have collapsed," she told the Post. "There are still people under the rubble. It's the middle of the night -- they can't get to them."
At least 7,100 people, including 461 children, have died since the uprising began in March, the Local Coordination Committees, a network of opposition activists, said. The United Nations said in January 5,400 had been killed but stopped counting, saying it was too difficult to confirm the toll.
Celebrity Couples of 2014 [PHOTOS]