The US and Russia say world powers will meet in New York on Friday to pass a UN resolution endorsing the Syria peace process.
It follows talks in Moscow between US Secretary of State John Kerry, his Russian counterpart Sergei Lavrov and President Vladimir Putin.
Mr Lavrov said both sides would keep working on contentious issues, like the make-up of the opposition delegation.
Mr Kerry said they had reached some agreement, such as on terrorist groups.
Russia launched an air campaign to bolster Mr Assad's government in September. It says it has targeted only "terrorists", above all jihadist militants from the Islamic State (IS) group, but activists say its strikes have mainly hit Western-backed rebel groups.
Friday's meeting in New York would pass a UN resolution reaffirming the principles of the peace process agreed in Vienna last month, Mr Lavrov said.
Mr Kerry travelled to Moscow to try to bridge gaps over ways to end the Syrian conflict.
He told President Putin the two countries had "the ability to make a significant difference".
The US and Russia disagree on what role Syrian President Bashar al-Assad should play in any transition.
The US wants him to stand down, but Russia says only the Syrian people should decide his fate.
Conflicting messages - Steve Rosenberg, BBC News, Moscow
There has been some confusion (to put it mildly) about whether Russia is or isn't supplying weapons and ammunition to the Free Syrian Army (FSA).
Last week, President Putin said it was - then, a few hours later, his spokesman Dmitry Peskov denied it.
On Monday, the chief of the Russian general staff said Russia was supporting the FSA with arms, ammunition and material help (copying Mr Putin almost word for word). But a few hours later a Kremlin aide denied that Moscow was supplying anything.
I used the Tuesday morning conference call with the Kremlin to try to get some clarity. Alas, I failed. This is what Mr Peskov said: "I have nothing to add to what's already been said. I have nothing to add and I don't want to explore this subject." No harm in trying.
"Together, we are looking for ways out of the most urgent crises,'' Mr Putin said ahead of the meeting.
A US-led coalition has been targeting IS positions in Syria since September 2014 and does not co-ordinate its raids with the authorities in Damascus.
"Even when there have been differences between us, we have been able to work effectively on specific issues," Mr Kerry said before the start of his talks with Mr Lavrov.
"The world benefits when powerful nations can find common ground," he added.
Mr Kerry has been comparing notes with the Russians on a meeting in Riyadh last week that united elements of the Syrian political and armed opposition.
Russia took issue with the outcome - a statement of principles to guide peace talks that says President Assad and his aides can play no part in any transitional period.
Russia also sees some of those who participated as terrorists, and it wants all parties to agree on a terrorist blacklist before proceeding further, our correspondent says.
The BBC's Barbara Plett-Usher, who is travelling with Mr Kerry, says he knows the Russians are indispensable because it is they who could bring Mr Assad to the negotiating table.
On Islamic State, Mr Kerry said Russia and the US agreed it was "a threat to every country".
Mr Lavrov said the IS issue was not limited to Syria, as the group was also active in Iraq, Afghanistan and Yemen.
He also said the meeting would cover the matter of Ukraine, with its continued division between the Western-backed government in Kiev and the Russian-backed separatists in its east.
Mr Kerry said: "Nothing would please us more than to solve the problem of Ukraine and move forward on the economic front."
Divisions over Assad's future
The United States, which supports the Syrian opposition, wants a negotiated settlement based on the 2012 Geneva Communique, which calls for the formation of a transitional governing body. It says President Bashar al-Assad must go.
Russia, which launched an air campaign against Mr Assad's opponents in September, also calls for the implementation of the Geneva Communique. But it says Mr Assad's future is for the Syrian people, and not external powers, to decide.
Most of Syria's political and armed opposition factions now agree on the need for a managed transition, but they demand that the president leave at the start of it.
Bashar al-Assad says peace talks cannot begin until "terrorism" is eliminated, and that his departure is out of the question before elections are held.