"Russia needs to understand that our patience is not infinite, in fact it is very limited with whether or not Assad is going to be held accountable," Kerry said during a visit to Norway.
"We also are prepared to hold accountable members of the opposition" who have been involved in continuing violence, he said after a meeting with his Iranian counterpart Mohammad Javad Zarif.
World powers have failed to turn a fragile cessation of hostilities in Syria, in effect since February 27, into a durable truce and Damascus has stepped up its military campaign against the Islamic State group and rebels in the second city of Aleppo.
"This is a critical moment and we are working very, very hard to see if we can in the next week or two come to an agreement that has a capacity to more fully implement a ceasefire across the country and deliver humanitarian access in a way that then provides for a genuine opportunity to bring people to the table and start talking about a transition," Kerry said.
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Kerry's talks with Zarif follow a meeting between the defence ministers of Iran, Russia and Syria last week on the battle against the various armed groups fighting the Assad regime.
Russia launched air strikes in support of the government in September.
The United Nations says nearly 600,000 Syrians live in besieged areas of Syria, most surrounded by government forces.
Earlier this month, the UN said the Syrian government had granted preliminary aid access to 15 of 18 besieged areas.