North Korea has emerged as one of the greatest foreign policy challenges for US President Donald Trump.
Kim Jong-un's North Korean government has conducted five nuclear tests and is also in the process of developing nuclear-tipped missiles that can reach the United States.
Over the weekend, a US official tipped the media that a United States Navy strike group led by a nuclear-powered aircraft carrier was on its way towards the western Pacific as a show of might.
On his first visit to Russia as Secretary of State, Tillerson will hold talks, Sergei Lavrov, his Russian counterpart.
The talks will be held on Wednesday, and they come at a time when relations between Moscow and Washington are languishing at a post Cold War low.
And in a statement before Tillerson's arrival, the Russian foreign ministry that it was concerned about many facets of US foreign policy, including on Yemen, Libya and Syria.
Of particular concern to the Kremlin, however, is North Korea.
"We are really worried about what Washington has in mind for North Korea after it hinted at the possibility of a unilateral military scenario," the statement said.
On Friday, Russia criticized US cruise missile strikes on a Syrian airbase, terming them an illegal attack on a sovereign state.
Russia is increasingly concerned that Donald Trump, whom it viewed as an isolationist, is increasingly becoming confident that force can help him achieve his foreign policy goals.