Putin said the leaders in St. Petersburg were split nearly "50-50" over whether to intervene militarily.
He said that action against Syria without U.N. Security Council approval would be illegal. Russia and China, which has also opposed military intervention in Syria, have veto power.
But that need not rule out action, U.S. State Department spokeswoman Marie Harf told reporters Friday. "We cannot allow Syria to act with impunity because one or two countries refuse to hold them accountable in the Security Council," she said.
The Syrian government has said that opposition fighters launched the attack on the outskirts of Damascus.
The United Nations has said more than 100,000 people -- including many civilians -- have been killed since a popular uprising spiraled into a civil war in 2011. That toll rose Friday, with the opposition Local Coordination Committees of Syria reporting at least 64 people killed nationwide.
Tensions affect some U.S. staff in Lebanon, Turkey
As tensions ratchet up over Syria, the U.S. State Department on Friday ordered the withdrawal of nonessential personnel from the U.S. Embassy in Beirut, Lebanon, and authorized nonemergency staff to leave a consulate in Adana in southern Turkey.
"Given the current tensions in the region, as well as potential threats to U.S. government facilities and personnel, we are taking these steps out of an abundance of caution to protect our employees and their families, and local employees and visitors to our facilities," a statement said.
Many observers fear that the civil war in Syria, which has become increasingly sectarian in nature, could spill into neighboring countries.
The State Department also issued revised travel warnings Friday for Lebanon and Turkey, both of which share a border with Syria.
It urges U.S. citizens to "avoid all travel to Lebanon because of current safety and security concerns" and to be "alert to the potential for violence" if traveling to or living in Turkey.
Many in Lebanon worry that the involvement of the Lebanese Shiite militant group Hezbollah in Syria's civil war could destabilize their own nation.
Lebanon has been shaken by a series of deadly bombings in recent weeks, including a blast in a Hezbollah stronghold in Beirut.
Al-Assad warned this week that a regional war could break out if Syria is attacked.
"The Middle East is a powder keg, and the fire is approaching today," he told French newspaper Le Figaro in an interview Monday.
Obama pushes for congressional action
Obama is seeking congressional approval for possible U.S. military strikes against Syria, although no vote is expected until after lawmakers reconvene from recess on Monday.
The president said Friday that he had expected skepticism from the public and from lawmakers.
He knew it was going to be "a heavy lift" when he announced Saturday that he was putting the proposal before Congress, he said, with some lawmakers foreseeing a "slippery slope" toward a prolonged U.S. involvement in Syria.
"For the American people who have been through over a decade of war now, with enormous sacrifice of blood and treasure, any hints of further military entanglement in the Middle East are going to be viewed with suspicion," Obama said. "That suspicion will probably be even stronger in my party than in the Republican Party."