Opening talks in Moscow with Russian Foreign Minister Sergey Lavrov before seeing President Vladimir Putin, Kerry said the world benefits when great powers agree in their approaches to major crises.
"Even when there have been differences between us, we have been able to work effectively on specific issues," Kerry said as he began a series of what are expected to be difficult discussions in the Russian capital. "Today, I hope we can find some common ground."
The results of today's meetings will determine whether or not a new international diplomatic conference on Syria will go ahead as planned at the United Nations on Friday.
On Ukraine, the two countries are split over the implementation of a February agreement meant to end hostilities between the Kiev government and Russian-backed separatists in the east.
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Lavrov noted "outstanding issues" on steps ahead in the Syrian political transition that is supposed to bring representatives of President Bashar Assad's government together with the opposition for negotiations by early January.
Kerry praised Moscow for having been "a significant contributor to the progress that we have been able to make" on Syria and said the US and Russia both believe the Islamic State group must be eliminated.
"Russia and the United States agree that this is a threat to everybody, to every country," he said. "They are the worst of terrorists. They attack culture and history and all decency. It leaves no choice but for civilized nations to stand together, to fight and destroy them."
It also complained that the US was unwilling to engage in "full-fledged coordination" between the two powers' militaries while both are conducting airstrikes in Syria.
Russia says its airstrikes since late September have targeted the Islamic State, but Western governments claim mostly moderate rebels are being hit and that Moscow is primarily concerned with shoring up Assad.