"It is necessary for Russia to take the first step to de-escalate the situation in eastern Ukraine," Tillerson said as he made his first visit as Washington's top diplomat to Kiev.
"We are disappointed by the lack of progress under the Minsk agreement," he added at a joint briefing with Ukrainian President Petro Poroshenko after they held talks.
"We do call on Russia to honour its commitments," Tillerson said, referring to a peace deal aimed at halting the conflict between Ukrainian government forces and Russia-backed rebels.
More than 10,000 people have been killed since the pro-Russian insurgency began in April 2014, which Kiev and the West accuse Moscow of orchestrating.
The US and the European Union have imposed sanctions on Russia, though Moscow has denied backing the rebels.
Efforts to secure a peace deal have foundered as the fighting has dragged on, and neither side appears prepared to make concessions.
Tillerson's visit to Ukraine followed a first face-to-face meeting between US President Donald Trump and Russian leader Vladimir Putin on Friday at the G20 summit in Hamburg, Germany.
The conflict as well as Russia's annexation of Crimea from Ukraine in 2014 have pushed ties between Moscow and the West to their lowest point since the Cold War.
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