Senior officials travelling with 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.
"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.
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.
Kerry and Lavrov have continued to meet, most recently on Sunday and Monday on the sidelines of the G20 in China, where Putin also talked to US President Barack Obama.
But fighting has continued on the ground, with Assad's Russian-backed forces encircling and attempting to choke rebel-held areas of Syria's biggest city, Aleppo.
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