US Secretary of State John Kerry has warned Syrian President Bashar al-Assad that seeking military gains will not end the civil war.
Mr Kerry said there would be "repercussions" if the Syrian government flouted a cessation of violence agreed in February.
A resurgence in fighting, particularly in the northern city of Aleppo, has threatened to derail the partial truce.
More than 250 people have been killed in Aleppo in the past 10 days.
As diplomatic efforts intensified on Tuesday, Russian Foreign Minister Sergei Lavrov said a unilateral truce declared by the Syrian military could be extended to Aleppo "in the next few hours".
After talks with UN envoy Staffan de Mistura in Moscow, he said Russia was working with the UN and US to include Aleppo in the "regime of calm" that has covered Damascus and Latakia since Saturday.
On Tuesday, 19 people were killed by rebel rocket fire in government-controlled areas of Aleppo, monitoring group the Syrian Observatory for Human Rights said.
State media said a hospital was hit, killing three people and wounding 17.
Last Wednesday, an air strike on a hospital in a rebel-held area killed 55 people. The US blamed the attack on government forces.
Speaking in Washington, Mr Kerry said he was hopeful the cessation of violence could be restored, and he warned President Assad of consequences if violations continued.
"If Assad does not adhere to this, there will clearly be repercussions, and one of them may be the total destruction of the ceasefire and then go back to war. I don't think Russia wants that," he said, foreign media reports.