In a phone call with US Secretary of State Tillerson, Lavrov "stressed the unacceptability of an escalation of tensions on the Korean peninsula, which the American military preparations in the region are leading to," the foreign ministry said in a statement.
Russia's top diplomat "called for resolution of differences exclusively through diplomatic methods."
US President Donald Trump said on Saturday that diplomatic efforts with North Korea have consistently failed.
He also tweeted last week that Tillerson was "wasting his time trying to negotiate" and added that: "only one thing will work!"
The US and its ally South Korea staged drills in September near the heavily-fortified border with North Korea.
China has proposed a plan, which Russia has backed, in which North Korea would suspend its nuclear weapons programme in return for the United States halting its military drills in the region.
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