"We have certainly made clear that our interest in Syria is not the end of any kind of Russian influence," deputy national security advisor Ben Rhodes told reporters, ahead of Putin's talks with Obama in Mexico on Monday.
"Our interest in Syria is an end to the violence that's being committed against the Syrian people and a government that reflects the will of the Syrian people," Rhodes said, adding that for such a scenario to unfold, Assad needed to leave power.
"If Syria continues to have a relationship with Russia, if Russia continues to have, again, a close relationship with the future government of Syria, that would be in the natural decision-making of two sovereign nations."
"It's not our goal in Syria to eliminate Russian influence."
Rhodes said that Washington was still checking into earlier reports, by NBC News citing a US official, that Moscow had sent armed troops to Syria to guard its deep-water port and military base in the Syrian city of Tartus.
Earlier Friday, Moscow denied discussing Assad's departure with Western nations in a move seemingly meant to quash reports from several major capitals about a shift in Russia's approach that acknowledged Assad's days were limited.
The French foreign minister said on Friday that Russia views Assad as a "tyrant" while a US State Department spokeswoman said a day earlier that "the Russians have also talked about" a political transition in Syria.
"If this was really said, this is not true," Lavrov said in reference to US State Department spokeswoman Victoria Nuland's comments.
"There were no such discussions and there could not have been such discussions. This completely contradicts our position," he told reporters.
Analysts say that Russia's position on Syria is partly motivated by its experience in Libya, when it decided not to block a UN-mandated no fly zone, only to see Western nations help push dictator Moamer Khadafi from power.
Lavrov was speaking a day after meeting US Deputy Secretary of State Bill Burns in Kabul for talks that Washington said touched on a transition in Syria modeled on the one adopted for Yemen in the past year.
Nuland on Friday billed Obama's talks with Putin on the sidelines of the G20 summit in the Mexican resort of Los Cabos as a "good opportunity" to discuss differences between the two governments over Syria.