Lavrov said the two sides "discussed the state of our bilateral relations ... including some specific irritators that have been in place."
And he stressed the importance of avoiding any actions that could ramp up tensions between the two countries, noting that resolving many top international issues "depends on our joint efforts."
On Iran, Kerry said the U.S. and Russia remain "closely aligned in this effort," stressing that continued cooperation would be crucial to sealing a deal with Iran in the final weeks of negotiations.
The U.S. and Russia also plan to work closely in the coming weeks to discuss finding a political solution to the Syrian conflict, which the U.S. has stressed can only happen if Syrian President Bashar el-Assad leaves.
Kerry met separately with Lavrov after his meeting with Putin.
Shortly after his arrival, Kerry joined Lavrov in laying a wreath at the Zakovkzalny War Memorial in Sochi for soldiers killed in World War II. The tribute followed a weekend of events to commemorate the 70th anniversary of the defeat of Nazi Germany.
Kerry drew on that moment in his remarks later Tuesday, calling the ceremony "a powerful reminder of the sacrifices that we shared to bring about a safer world and what our nations can accomplish when our peoples are working together toward a same goal.