Interfax news agency quoted a Syrian opposition figure as saying on Tuesday that Russia’s call not to discuss the future of the Assad regime could halt peace negotiations.
Russian Deputy Foreign Minister Sergei Ryabkov announced that the Kremlin's opinion that Assad's future should not be discussed for now has found understanding in Washington.
On this issue, Riad Nassan Agha, a member of the opposition High Negotiations Committee (HNC), told Interfax and underlined that, "It is obvious that this statement aims to stop the process of negotiations and to deprive the High Negotiating Council of any hope to continue the talks."
"What else are we going to discuss if we are not going to discuss Assad's fate?" he said.
However, US State Department spokesman Kirby reiterated the US's view on removing Syrian regime leader Bashar al Assad from power after Russia claimed they agreed not to discuss his future.
Secretary of State John Kerry visited President Vladimir Putin and other Russian officials in the Kremlin last week to plan the next steps they will take.
Russia and the United States agreed at the talks on March 24, to use their influence over the opposite sides in the Syrian conflict to speed up progress towards a political solution.
The US softened demands last year for Assad's immediate departure, but still insists he should resign at some point in a political transition process.
Russia says outside powers shouldn't try to determine Syria's leadership.
Assad has offered no indication he is willing to leave power.