Speaking at a meeting with European foreign ministers in Vienna on December 7, Tillerson said the United States will not lift sanctions against Russia until it pulls its forces out of eastern Ukraine and Crimea.
"The issue that stands in the way is Ukraine," Tillerson said at a news conference after the Organization for Security and Cooperation in Europe (OSCE) ministers meeting.
"We can have differences in other arenas.... But when one country invades another, that is a difference that is hard to look past or to reconcile," he said.
"And we've made this clear to Russia from the very beginning: That we must address Ukraine, it stands as the single most difficult obstacle to us renormalizing relations."
After Tillerson's strong statement on Ukraine, a face-to-face meeting with his Russian counterpart appeared to produced no breakthroughs on points of tension between the two countries.
"I'm not going to tell you specifically what we get. We get progress, that's what we get," Tillerson said in the Austrian capital on December 7 following his talks with Russian Foreign Minister Sergei Lavrov.
"We get dialogue, we get cooperation, we don't have it solved. You don't solve it in one meeting," he added.
The United States and the European Union are pushing Moscow to allow a robust United Nations peacekeeping force to be deployed to eastern Ukraine, where Russia-backed separatist militia are fighting government forces in a conflict that has killed more than 10,000 people since it started in April 2014.
Lavrov said he told Tillerson that Moscow was "concerned about attempts to turn our initiative about a deployment of UN guards to ensure OSCE [Special Monitoring] Mission's security upside-down."
As it was reported earlier, Pavlo Klimkin, the Minister of Foreign Affairs of Ukraine spoke at the 24th session of the foreign ministers of the OSCE on December 7. He drew special attention to the issue of the Russian aggression and necessity to find the efficient mechanisms of the fights against it.
Klimkin noted that the world community should concentrate on three directions due to this: to hold the efficient fight against terrorism and cyber-attacks sponsored by Russia; to expend the efforts to oppose the Russian propaganda and to continue the protection of the human rights and fundamental freedoms.
Ukrainian minister urged the OSCE to strengthen the pressure on Russia by the personal sanctions. According to Klimkin, the speeches of the EU, the US delegation, and Austrian chairmanship began with the issue of the Russian aggression against Ukraine.