"It is necessary for Russian Federation to take the first steps to de-escalate the situation in the eastern part of Ukraine", Tillerson told reporters at a joint news conference in Kiev with Ukrainian President Petro Poroshenko.
"At the request of President (Vladimir) Putin, the United States has appointed. a special representative for Ukraine, Ambassador Kurt Volker", Tillerson told reporters after a meeting between Putin and U.S. President Donald Trump on the sidelines of the G20 summit in Hamburg, Germany.
According to the president, Ukraine is not interested in delaying such negotiations, because "Ukraine pays a high price - its heroes are wounded and killed" every day. Russian Federation annexed the Crimean Peninsula from Ukraine in 2014.
"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.
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The team said it was a brake disk failure and Hamilton's mechanics worked frantically to get his auto ready for qualifying . However, the three-time world champion is less confident that he can perform similar heroics this time around.
"Kurt's wealth of experience makes him uniquely qualified to move this conflict in the direction of peace", Tillerson said in a statement.
"The US and European Union sanctions on Russian Federation will remain in place until Moscow reverses the actions that triggered these particular sanctions", Tillerson said at a briefing after a meeting with Ukrainian President Petro Poroshenko in Kiev.
Moscow has repeatedly said the Ukraine crisis is an internal conflict and that Kiev is not fulfilling its part of the Minsk agreements and refusing to negotiate with its own people in Donbass.
Poroshenko hailed United States involvement and reiterated Tillerson's commitment to seeking a negotiated peace deal. "We want to acknowledge that, (but) we still have more to do", he said.
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Mr Putin said on Saturday that he was sure the interests of Ukrainians and Russians "coincide fully" and that only the "Russophobic" attitude of Kiev's leaders had put the neighbours at odds.
Tillerson also commented on another key bone of contention between Trump and Putin at the G20: allegations of Russian interference in U.S. election campaign, in favour of the Republican candidate.
The situation in Ukraine and its resolution were expected to be on the agenda during the first face-to-face meeting between Putin and Trump in Hamburg on Friday.
"In all candidness, we did not expect an answer other than the one we received", he said Sunday.
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The training mission occurred the day before President Trump and Chinese President Xi met at the G-20 summit in Germany. Such actions, however, may do little to sway China or deter it from boosting its military presence in the region.
He called the initial dialogue an effort to "explore a framework under which we might begin to have agreement on how to deal with these very complex issues of cyberthreats, cybersecurity, cyberintrusions".