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Tillerson has been well informed about Moscow's aggression against Ukraine, and various options for resolving the crisis have been discussed with him, according to Klimkin.

The minister added that the United States is likely to join Ukraine, Germany and France in negotiations with Russia, but stressed that it is not the format of negotiations that matters, but their effectiveness.

Read alsoTillerson to discuss Ukraine, Syria with Lavrov on May 10Klimkin will remain in Washington until late Wednesday, when Rex Tillerson will be meeting with Russian Minister Sergei Lavrov to discuss Ukraine and Syria. The Ukrainian side was not invited to the talks, but the U.S. promised to stand by Kyiv’s side.

"Not only does he understand the general logic of our common position, he also understands the details. now it's up to him to put pressure on Lavrov, I really hope that he will succeed ... We talked in great detail on the phone, maybe it's worth meeting following the latest contacts with the Russian side," Klimkin said.