WASHINGTON, Sept 12- US Secretary of State Rex Tillerson believes the diplomatic tiff between Russia and the United States should not be escalated further and hopes the two countries can begin working to improve ties, a State Department spokeswoman said on Tuesday."I think the secretary believes that no further escalatory action is necessary at this point and we look forward to trying to forge ahead," State Department spokeswoman Heather Nauert told a briefing after being asked the possibility of further diplomatic cuts by the two sides.Nauert also noted that Ambassador Joseph Yun, the US special representative for North Korean policy, was in Moscow on Tuesday for talks with Russian officials about efforts to curb Pyongyang's nuclear and missile programs.