The US and Russia have discussed the possibility of "localised ceasefires" in Syria ahead of peace talks to be held in Switzerland next week.
Russia also said that Syria was considering opening humanitarian access to besieged rebel areas.
US Secretary of State John Kerry, and Russian Foreign Minister Sergei Lavrov, met in Paris to discuss arrangements for the Geneva talks.
Mr Kerry said that he and Mr Lavrov "talked today about the possibility of trying to encourage a ceasefire. Maybe a localized ceasefire, beginning with Aleppo," Syria's largest city.
“Both of us have agreed to try to work to see if that could be achieved."
Syrian rebels backed by Washington have agreed that, if the government commits to such a partial ceasefire, "they would live up to it", Mr Kerry said.
Given the history of failed attempts to end the war, which has killed more than 100,000 people and displaced millions, it remains far from clear that even a partial ceasefire can be achieved or if it can hold.
It also seems unlikely to be honoured by powerful militant Islamist rebel factions, some of whom are at war with both Damascus and other rebel groups backed by the West and Gulf states.
But diplomats are trying to persuade the combatants to agree to a series of steps to improve the atmosphere for Syrian peace talks planned for Switzerland on 22 Jan.
Mr Lavrov, whose government backs Mr Assad, said the Syrian government had indicated it might provide access for humanitarian aid to reach besieged areas.
He specifically cited the Damascus suburb of the east gate, where 160,000 people have been largely trapped by fighting, according to the United Nations.
"We await similar steps by the opposition," Mr Lavrov said.
Mr Kerry expressed some scepticism that Mr Assad's government would follow through.
"The proof will be in the pudding, as we say," he said. "This news of a possibility is welcome."
Mr Kerry said he and Mr Lavrov had also discussed a possible exchange of prisoners between the sides.
The opposition is ready to put together a list of prisoners and "are prepared to entertain such an exchange", he said.
Divisions over Iran
But both Russia and the United States remained sharply divided over whether Iran, which is a major player in the Syria conflict, should attend the peace talks.
"I'm convinced that practicality and pragmatism ... require that Iran should be invited," Mr Lavrov said.
Other countries have already been invited "who do not want the conference to succeed", he said, in apparent reference to Gulf Arab countries who are arming rebel groups.
"Iran's participation or non-participation is not a question of ideology. It is a question of practicality and common sense," John Kerry said.
"I invite Iran today to join the community of nations, the 30 nations that are already prepared to come, and be a constructive partner for peace," he said. "That's the invitation."
The main Syrian opposition group backed by the West has said it will decide on Friday whether to attend the peace conference, known as Geneva 2.