Story highlights John Kerry is expected to meet with Russian President Vladimir Putin, as well as Russia's foreign minister

"It's important to try to talk to the senior decision-maker," a State Department official says

Moscow (CNN) U.S. Secretary of State John Kerry met Tuesday with Russian President Vladimir Putin and other top Russian officials, when he paid his first visit to Russia in two years at a time of severely strained relations between the two powers.

Kerry and Russian Foreign Minister Sergey Lavrov discussed everything from Iranian nuclear negotiations to cooperating on a solution to the Syrian and Ukrainian conflicts, and also touched on the situation in Yemen. The pair also broached tensions between the U.S. and Russia and both stressed the need to improve cooperation.

Kerry seemed optimistic on that front, saying positive things about U.S.-Russia cooperation on key issues and also affirming that the U.S. and the European Union could begin rolling back sanctions on Russia if the Minsk agreements to stop the fighting in Eastern Ukraine are implemented.

"There is no substitute for talking directly to key decision makers, particularly during a period that is as complex and is moving as this is," Kerry said Tuesday, adding that he was grateful for the "significant amount of time" Putin spent with him.

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Lavrov said the two sides "discussed the state of our bilateral relations ... including some specific irritators that have been in place."

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