Those two countries, powerful allies of Syria's, have vetoed two previous council resolutions, saying that they were unbalanced and that they demanded only that the government, not the opposition, stop attacks.
Moscow accused Western powers of fueling the conflict by backing the rebels.
It was discussed behind closed doors by the five permanent council members - the U.S., Russia, China, Britain and France - along with Morocco, the Arab representative on the council. U.S. Ambassador Susan Rice appeared downbeat as she left the meeting, saying, "I don't think you should expect anything specific."
According to Syrian state news agency SANA, Assad said that "the Syrian people, who have in the past managed to crush foreign plots . . . have again proven their ability to defend the nation and to build a new Syria through their determination to pursue reforms while confronting foreign-backed terrorism."
His crackdown has turned to southern Daraa province, where the uprising began a year ago. Troops shelled a village in Daraa and clashed with military defectors.
Activists said the military blasted a bridge and a tunnel near the border with Lebanon that have been used as escape routes for the wounded and refugees fleeing central Homs province, an opposition stronghold that just endured a heavy monthlong offensive.
Rupert Colville, spokesman for the U.N. High Commissioner for Human Rights in Geneva, described video that has emerged of torture victims allegedly shot secretly in the Military Hospital in Homs as "truly shocking."
The video, broadcast this week on Britain's Channel 4, shows wounded civilians blindfolded and chained to their hospital beds, some with clear torture marks on their bodies, allegedly at the hands of medical staff.
The international outcry against Syria has grown louder by the day. On Monday, McCain called for air strikes against the country, saying the United States has a moral and strategic obligation to force out Assad and his loyalists.
Obama has resisted calls to step into the turmoil in Syria to stop Assad's bloody crackdown. At a news conference Tuesday, he said the international community had not been able to muster a campaign against Syria like the one in Libya that ousted longtime strongman Moammar Gadhafi last year.
"For us to take military action unilaterally . . . or to think that somehow there is some simple solution, I think is a mistake," Obama said. "What happened in Libya was we mobilized the international community, had a U.N. Security Council mandate, had the full cooperation of the region, Arab states, and we knew that we could execute very effectively in a relatively short period of time. This is a much more complicated situation."
Obama's strategy has been to use sanctions and international diplomatic isolation to pressure Assad into handing over power.
Marine Gen. James Mattis, head of U.S. Central Command, told the Senate Armed Services Committee that the advanced air defense weapons Russia has provided to Syria would make it difficult to establish a no-fly zone there as part of an effort to help the rebellion.