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[GENEVA] US Secretary of State John Kerry flew in to Geneva on Friday to meet his Russian counterpart once again, seeking a deal with Moscow to restore a ceasefire in Syria.
Senior officials travelling with Mr Kerry said he would not have travelled to join Foreign Minister Sergei Lavrov unless he thought there was a chance of making progress.
But they warned they could not guarantee a final agreement would be reached within the narrow window available before both men return home later in the day.
Washington wants concrete steps from Russia to force its Syrian ally Bashar al-Assad to stop bombing his own people and to lift the siege of the city of Aleppo.
"We need to see a situation where it's clear within whatever is being agreed with the Russians that there won't be a siege of Aleppo," a senior US official told reporters.
"If we conclude that we can get there then we'll keep going," he said, suggesting the marathon negotiation could be prolonged still further, but not indefinitely.
"If we conclude that it's being dragged on for no other purpose than to gain time then there'll be no purpose in us continuing," he warned.
In exchange for reining in its client in Damascus, Russia wants closer military cooperation with the United States in the battle against jihadist groups fighting in Syria.
This would help its jets target the Islamic State and Nusra Front groups, while giving it de facto political cover as a partner working more closely alongside US forces.
Asked whether a deal was possible on Friday, another senior US official said: "All I can say is we can't guarantee at any point that we are on the cusp of finishing".
"That said, I think that if we didn't think ... that there remained a possibility of getting this done, we wouldn't be going back to Geneva," he added.
Washington and Moscow are joint leaders of the international effort to end the Syrian civil war, and declared a UN-backed ceasefire as far back as February.
But the truce collapsed and President Vladimir Putin's Russia has maintained strong support for Mr Assad's forces, while Washington has encouraged the opposition rebels.
Mr Kerry and Mr Lavrov have continued to meet, most recently on Sunday and Monday on the sidelines of the G20 in China, where Mr Putin also talked to US President Barack Obama.
But fighting has continued on the ground, with Mr Assad's Russian-backed forces encircling and attempting to choke rebel-held areas of Syria's biggest city, Aleppo.