TEHRAN, Young Journalists Club (YJC) -Americans want “to see Russia take steps to improve relations with the United States," Tillerson said in a statement on Saturday.
"We hope that there will be cooperation between our two countries on major global issues and these sanctions will no longer be necessary," Tillerson added.
Tillerson said the Trump administration would work to make sure its "messages" to the countries were "clearly understood."
"We will work closely with our friends and Allies to ensure our messages to Russia, Iran, and North Korea are clearly understood," he said.
Tillerson's statement comes a day after the White House said Trump would sign a bill imposing fresh sanctions against Russia, Iran and North Korea.
"President Donald J. Trump read early drafts of the bill and negotiated regarding critical elements of it," White House press secretary Sarah Huckabee Sanders said in a statement Friday night, adding, "He has now reviewed the final version and, based on its responsiveness to his negotiations, approves the bill and intends to sign it".
Russia has already retaliated against the US-led sanctions imposed over the Ukraine crisis and claims of interference in the 2016 presidential election, demanding the closure of US property in Russia and staff reductions for US diplomatic personnel.
The Russian Foreign Ministry said in a statement on Friday that Moscow was prepared to mend broken relations with the US based on "mutual respect and balance of interests".