The Russian foreign ministry said in a statement that Lavrov told Tillerson in a phone call on Tuesday that political and diplomatic tools should be used to find a peaceful solution to the North Korean nuclear crisis. He also reaffirmed the USA readiness to protect the United States and its allies by "using the full range of diplomatic, conventional, and nuclear capabilities at our disposal".
North Korea has staged 14 missile tests since the beginning of the year, including nine that took place since the new South Korean leader came into office.
Russia's Foreign Ministry says USA security forces plan to search the building after it is vacated.
Declaring that "enough is enough", Haley said existing measures not worked and accused North Korean leader Kim Jong-Un of "begging for war" with the country's sixth and most powerful nuclear test. North Korea regularly issues apocalyptic warnings to the US and its allies.
Weapons experts say it's nearly impossible to verify if the warhead and missile could be successfully paired unless North Korea were to fire a nuclear-tipped ICBM.
Ahead of his meeting with Putin, Moon said the situation could get out of hand if North Korea's missile and nuclear tests aren't stopped.
Trump has grown increasingly frustrated with the response of other countries to North Korean provocations.
Diplomats have said the Security Council could consider banning North Korean textile exports, barring its airline and stopping supplies of oil to the government and military.
The Trump administration last week ordered the closure of three Russian facilities in the US: The San Francisco consulate and trade missions in NY and Washington.
Members of the Japanese parliament and Germany's Chancellor Angela Merkel have also demanded tougher United Nations sanctions on North Korea.
Analysts say it is most likely North Korea will carry out its next "provocative" act on or around September 9th when the country celebrates its founding day.
Since the Korean War, Beijing has avoided prodding North Korea to the point it might collapse, fearing a destabilising economic blow and the possibility of the U.S. military gaining influence on its border via a unified Korea.
The Russian president's spokesman, Dmitry Peskov, confirmed that the two leaders discussed the situation on the Korean Peninsula in view of the latest nuclear bomb test conducted by Pyongyang.