"The issue that stands in the way is Ukraine," Tillerson said.
The assessment from America's top diplomat notably played down other areas of dispute, particularly Russia's meddling in the 2016 presidential election. US intelligence agencies, including the CIA and FBI, have concluded the Kremlin interfered in the election in an effort to help now-President Donald Trump and hurt Democrat Hillary Clinton.
Trump has repeatedly cast doubt on that finding, and a special counsel is investigating whether members of the Trump campaign colluded with the Russian effort. He has said he believes Russian President Vladimir Putin's personal denials that Moscow meddled.
Tillerson's focus on Ukraine came as he met with European diplomats at the Organisation for Security and Cooperation in Europe, established during the Cold War to serve as a bridge between East and West.
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Tillerson insisted the US could never overlook Russia's "attempted annexation" of Crimea or Moscow's military intrusion in eastern Ukraine.
"Russia is arming, leading, training and fighting alongside anti-government forces.