Opening talks with the Russian defence and foreign ministers, Kerry acknowledged that ties had faced "challenging moments" and said he hoped for a "candid" exchange of views.
"The relationship between the United States and Russia is, needless to say, a very important relationship and it is marked by both shared interests and at times colliding and conflicting interests," Kerry told reporters.
Kerry said that he and his Russian counterpart, Foreign Minister Sergei Lavrov, both played hockey.
"We both know that diplomacy like hockey and sometimes results in occasional collisions," Kerry said.
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Relations between the former Cold War foes deteriorated after Edward Snowden, an ex-contractor for the US government, flew to Moscow after revealing details of Washington's widespread surveillance on its citizens.
US President Barack Obama cancelled a summit with his counterpart Vladimir Putin in Moscow to protest Russia's decision to grant asylum to Snowden.
However, the two countries agreed to go ahead with the so-called two-plus-two meeting of foreign and defence ministers that will likely discuss issues including Syria, Iran and Afghanistan.