During a short visit to Poland ahead of the G20 summit in Hamburg, Germany, this week - on the sidelines of which he met with Russian President Vladimir Putin for the first time - U.S. leader Donald Trump called on Russia to "cease its destabilizing activities in Ukraine and elsewhere".
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.
Volker will "coordinate all State Department efforts to bring a resolution to the conflict created when Russian Federation invaded Crimea and later eastern Ukraine", Tillerson spokesman R.C. Hammond told Bloomberg.
"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.
Mr Trump tweeted on Sunday that he had "strongly pressed" Mr Putin about Russian interference in the United States election and had discussed with him the possibility of creating "an impenetrable cyber security unit".
"We do call on Russian Federation to honor its commitments that were made under the Minsk accords and to exercise influence over the separatists in the region that they have complete control over", Tillerson said, adding later: "The U.S. and European Union sanctions on Russian Federation will remain in place until Moscow reverses the actions that triggered these particular sanctions". Russian Federation annexed the Crimean Peninsula from Ukraine in 2014. The Kremlin has denied backing the separatists.
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U.S. State Department spokeswoman Heather Nauert said on July 5 that Tillerson would "reaffirm" Washington's "commitment to Ukraine's sovereignty and territorial integrity" and encourage Kyiv to continue implementing reforms to strengthen its "economic, political, and military resilience".
Earlier, the US state Department reported that the head of Department Rex Tillerson July 9, will pay a working visit to Kiev to meet with Poroshenko.
His appointment suggests Washington wants to play a bigger role in efforts to resolve the conflict in Donbas, which until now have centred on the so-called Normandy format of talks involving Ukraine, Russia, Germany and France.
When asked about the meeting on Sunday, Tillerson said, "In all candidness we did not expect an answer other than the one we received".
Secretary of State Rex Tillerson on Friday named a former North Atlantic Treaty Organisation ambassador and National Security Council director as the United States' special envoy to Ukraine.
"Ukraine has come a long way", he said.