The meeting was the first between the two since the sanctions were signed into law by Trump.
Numerous congressional probes are underway, while Special Counsel Robert Mueller has opened a grand jury investigation into whether Trump campaign aides illegally colluded with Russian interests on Trump's behalf in the election and whether Trump obstructed justice when he fired former Federal Bureau of Investigation chief James Comey, who was leading the agency's Russia probe before Mueller took over.
Russian Federation said recently it was forcing the U.S.to cut its embassy and consulate staff in Russian Federation by 755 people.
"Trying to help [Russia] understand just how serious this incident had been and how seriously it had damaged the relationship between the US and the American people and the Russian people", Tillerson said.
White House spokeswoman Lindsay Walters says Monday that Trump had an hour-long call with Secretary of State Rex Tillerson and Chief of Staff John Kelly.
Russian Foreign Minister Sergei Lavrov said on Sunday that Moscow "is ready to normalise its dialogue" with Washington if Washington abandons its "confrontational approach" with Moscow.
Tillerson says the US has deep differences with Russian Federation including on Ukraine, but that it's not a good idea to "just cut everything off on one single issue". They also seized two USA diplomatic properties.
"The best signal that North Korea could send that they're prepared to talk would be to stop these missile launches", he said, holding out the prospect of USA envoys sitting down with Pyongyang's isolated regime. "Still a lot to do".
The Trump administration named Volker to the position in July.
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Moscow vehemently denies any efforts to influence the United States election, and retaliatory sanctions passed by Congress last month - against President Trump's wishes - have sparked a tit-for-tat. Tillerson has made clear that he and Trump did not support the legislation, but would enforce it now that it's law.
Earlier Sergei Ryabkov said that it is important for Russian Federation to create a working economic system that would be less dependent on the USA dollar and on the U.S. financial system as a whole. Discussions are also continuing on expanding the U.S.
Both sides discussed Russia's countermeasures to USA sanctions.
"Naturally, such actions, including the illegal retention of our diplomatic property since December of a year ago, could not remain unanswered, and won't be in the future".
To date, more than 13.9 million Mir cards have been issued in Russia, to roughly 10 percent of the country's population, according to the Russian National System of Payment Cards.
"As for foreign policy, I am disappointed and have to state that in many respects this is a continuation of the worst of [Barack] Obama's legacy, even a tougher policy in some aspects, directions, the rhetoric and the political line, which caused problems in relations with us and problems in Washington's relations with other countries at the final stage of the previous administration's tenure", the diplomat noted.
If the two leaders discussed those or other USA concerns about Duterte's government, they didn't do so in public.
"I think, it is indicative of the importance that the United States pays and places upon this relationship with ASEAN", he said.
"However, North Korean representatives reacted in the same manner to all previously passed resolutions of the UN Security Council".