OSLO (AFP) -- US Secretary of State John Kerry warned Russia on Wednesday that US patience on the Syria conflict and the issue of President Bashar al-Assad's fate is running out.

"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.

Peace talks aimed at ending the five-year conflict have stalled and Damascus has stepped up its military campaign against the Islamic State group and rebels in the second city of Aleppo.

"It is very clear that the cessation of hostilities is frayed and at risk and that it is critical for a genuine cessation to be put in place. We know that, we have no illusion," Kerry said.

World powers have failed to turn a fragile cessation of hostilities in Syria, in effect since February 27, into a durable truce.

"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.

"I'm not going to make any promises to be delivered on but I do believe the conversation I had with Zarif indicates to me possibilities for how this could be achieved," he added, without elaborating.

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.

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.

Syria's war has killed more than 280,000 people and displaced millions since it started with the brutal repression of anti-government protests in March 2011.