Russian Foreign Minister Sergei Lavrov, speaking after meeting China's top diplomat, said Moscow and Beijing were committed to "the need to strictly adhere to the norms of international law...and not to allow their violation".
Russia and China have opposed military intervention in Syria throughout a 17-month-old revolt against President Bashar al-Assad. They have vetoed three U.N. Security Council resolutions backed by Western and Arab states that would have put more pressure on Damascus to end violence that has cost 18,000 lives.
The United States and its allies have shown little appetite for military action in Syria, in contrast to last year's NATO campaign that helped topple Libyan leader Muammar Gaddafi.
But Obama used some of his strongest language yet on Monday to warn Assad not to cross a "red line" of even shifting unconventional weapons in a threatening manner.
Seeking re-election in November, Obama noted that he had refrained "at this point" from ordering U.S. military engagement in Syria. But when he was asked at a White House news conference whether he might deploy forces, for example to secure Syrian chemical and biological weapons, he said his view could change.
"We have been very clear to the Assad regime, but also to other players on the ground, that a red line for us is (if) we start seeing a whole bunch of chemical weapons moving around or being utilized," Obama said. "That would change my calculus."
Syria last month acknowledged for the first time that it had chemical or biological weapons and said it could use them if foreign countries intervened. The threat drew strong warnings from Washington and its allies, although it is not clear how the Syrian armed forces might use such weapons in urban warfare.
"We cannot have a situation where chemical or biological weapons are falling into the hands of the wrong people," Obama said, adding he was not certain the stockpile was secure.
Obama has been reluctant to embroil the United States in another war in the Middle East and refuses to arm Syrian rebels, partly for fear that some of those fighting the Iranian-backed president are Islamist radicals equally hostile to the West.
Rebels have seized swathes of territory in northern Syria near Turkey, which now hosts 70,000 Syrian refugees.
Turkish Foreign Minister Ahmet Davutoglu was quoted as saying the United Nations may need to create a "safe zone" in Syria to accommodate those fleeing the fighting, saying his country would not be able to take in more than 100,000 refugees.
But creating a safe haven would require imposing a no-fly zone, an idea which U.S. Defense Secretary Leon Panetta said last week was not a "front-burner" issue for Washington.
When Obama was asked whether he envisioned the possibility of using U.S. forces at least to safeguard Syria's chemical arsenal, he said: "We're monitoring that situation very carefully. We have put together a range of contingency plans."
The U.S.-based Global Security website says there are four suspected chemical weapons sites in Syria producing the nerve agents VX, sarin and tabun. It does not cite its sources.
Israel, still formally at war with Syria, has also debated whether to attack the unconventional arms sites which it views as its gravest peril from the conflict next door.
Fighting raged on in Syria, killing around 200 people on Monday, the Syrian Observatory for Human Rights said, and a Japanese woman journalist died of wounds sustained in Aleppo.
U.N. military observers left Damascus after a four-month mission during which they became helpless spectators of the conflict, and activists said government forces launched air strikes near the capital that killed two dozen people.
The U.N. representatives blamed both sides for the collapse of a truce brokered by outgoing special envoy Kofi Annan: "Our mission failed because the two sides did not abide by their commitments," said one monitor, who declined to be named, before seven United Nations cars left a Damascus hotel carrying some of the last members of a mission once 300 strong.
Rebel fighters have complained that foreign powers have supplied neither the quantity or quality of weaponry they need to defeat Assad, such as anti-aircraft missiles.
While outgunned by Assad's forces, rebels still managed to seize control of districts in Damascus and Aleppo last month, as well as several border crossings and parts of the north, before the army counter-attacked in Syria's two main cities.
With diplomatic efforts to end the war stymied by divisions between world powers and regional rivalries, Syria faces the prospect of a prolonged conflict that increasingly sets a mainly Sunni Muslim opposition against Assad's Alawite minority.
That sectarian faultline also flared in neighboring Lebanon, where one person was killed overnight in the northern port city of Tripoli, a mainly Sunni Muslim city with a staunchly pro-Assad Alawite minority.
Gunmen in the Sunni district of Bab al-Tabbaneh and Alawite rivals in Jebel Mohsen exchanged sporadic gun and grenade fire through the night, despite the presence of Lebanese army troops.
The army said 10 soldiers were wounded, and residents and medics said 40 other people were also hurt.