The two diplomats spoke by phone on December 26 and "shared a common opinion that the nuclear-missile developments in [North Korea] violate the demands of the United Nations Security Council", according to a statement from the Russian Foreign Ministry.
Russian Foreign Minister Sergei Lavrov says he is "united in opinion" with his US counterpart Rex Tillerson on the issue of North Korea but that they differ on how to resolve the crisis over Pyongyang's nuclear weapons program.
While Tillerson voiced support for opening diplomatic dialogue between the two states, Trump said he would not take part in any talks with Pyongyang unless the isolated state agreed to give up its pursuit of nuclear weapons.
North Korea is preparing to launch a satellite, it has been claimed, as outside observers warn that the nuclear-armed regime's space programme is likely to be a cover up for more for weapons tests.More news: Firefighter's family loses home and Christmas gifts in house fire
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South Korea predicted today that their hostile neighbours would look to open negotiations with the United States next year in an optimistic outlook for 2018.
This may open the way for the de-escalation of tensions between the USA and North Korea, Peskov added.
"It was underlined that it is necessary to move from the language of sanctions to the negotiating process as soon as possible".
The UN Security Council unanimously voted to impose new sanctions on North Korea on Friday in response to its recent intercontinental ballistic missile test, a move North Korea called an act of war, tantamount to a complete economic blockade.
The measures order North Koreans working overseas to return home within two years and ban almost 90 percent of refined petroleum exports to the country.