"I think the secretary believes that no further escalatory action is necessary at this point, and we look forward to trying to forge ahead," Heather Nauert told a press briefing on September 12, RFE/RL reported.
The comments come during a period of heightened tensions between Washington and Moscow.
The United States on August 31 ordered the closure of Russia's consulate in San Francisco and two trade annexes in Washington, D.C., and New York, escalating a diplomatic tit-for-tat that followed Moscow's order for a sharp cut in U.S. diplomatic personnel in Russia.
Broader disagreement between the United States and Russia involve allegations by U.S. security agencies of Russia's interference in the 2016 U.S. president election; sanctions imposed by Western powers against Moscow for its annexation of Ukraine's Crimea Peninsula and its support for separatist forces in eastern Ukraine; and disputes over strategies to deal with Syria and North Korea.
Nauert cited a visit by Ambassador Joseph Yun, the U.S. special representative for North Korean policy, to Moscow for talks with Russian officials as a sign of continued cooperation in efforts to confront Pyongyang over its banned missile and nuclear programs.
She also pointed to Undersecretary Thomas Shannon's visit to Helsinki for meetings with Russian Deputy Foreign Minister Sergei Ryabkov.
Read alsoPOLITICO: Tillerson moves toward accepting funding for fighting Russian propagandaShe said the meeting was the third between the two diplomats, who have been charged by Tillerson and Russian Foreign Minister Sergei Lavrov to look to resolve disputes preventing wider cooperation between the two countries.
Nauert said she did not have any statement regarding any potential agreements from the talks.
The Russian Foreign Ministry said on September 11 that the talks focused on the "forced closure" of its consulate in San Francisco and the "illegitimate seizure" of trade annexes in Washington and New York.
U.S. officials say the United States has taken no improper diplomatic or law enforcement action in connection with the order for Russia to vacate the three diplomatic facilities by September 2.
Nauert did not comment on reports from Russian state-run TASS news agency that Tillerson will meet with Lavrov on the sidelines of the UN General Assembly session, which runs from September 12-25.