Tillerson, who will meet with his Moscow counterpart, Sergey Lavrov, later Thursday, said the U.S. will "never accept Russia's occupation and attempted annexation" of Crimea and will continue sanctions until the peninsula is returned to full control of Ukraine.
Tillerson is on a visit to Europe during which he has reassured allies with tougher rhetoric against Moscow than that of U.S. President Donald Trump, who has sought better relations with Russian President Vladimir Putin. Russian Federation denies accusations it fomented the conflict and provided arms and fighters.
Tillerson made no mention on Thursday of Russia's efforts to meddle in the United States' 2016 presidential election, though he hinted at such activities a day earlier in Brussels, saying that Moscow's efforts to "undermine Western institutions" remained an obstacle to warmer ties with North Atlantic Treaty Organisation.
"We should be clear about the source of this violence", Tillerson said, referring to increasing ceasefire violations recorded by the OSCE's Special Monitoring Mission of observers in eastern Ukraine.
But Western powers, led by the United States, want a force with a robust mandate that would allow it to protect the 600 OSCE monitors there, police ceasefire lines and investigate ceasefire breaches across eastern Ukraine.
Ideal conditions ahead for Geminid meteor shower, pairings of moon, planets
Unfortunately, under light-polluted skies, you won't be able to catch a glimpse of as many, as they won't be as clearly visible. Why is this year so favorable for the Geminids? The US is tipped to have prime astronomical conditions to view the shower.
Tillerson said the military alliance would not return soon to regular NATO-Russia Council meetings. "We call on Russian Federation and its proxies to end its harassment, intimidation and its attacks on the OSCE Special Monitoring Mission".
After long resisting the idea, Russia has suggested deploying a United Nations peacekeeping force to help end the war between Ukraine's government and Russian-backed separatists in the east of the country that has killed over 10,000 people since 2014.
Economic sanctions were placed on Russian Federation by then-US President Barack Obama in 2014 following the country's military action in Crimea and Ukraine.
He also made clear that Washington did not accept Russia's seizure of the Crimean Peninsula from Ukraine in 2014.
"We've reached an absolute low point regarding confidence between the main players", the Organization for Security and Co-operation in Europe's secretary general Thomas Greminger told reporters.