Tillerson spoke at a news briefing on August 1.
Donald Trump has heard the US intelligence assessments about Russian Federation taking steps to help put him in power, but the president refuses to believe it. Trump recently sat down with radical TV preacher Pat Robertson said, in reference to Russia's Vladimir Putin, "Why would he want me?" "I think the fact that they felt the need to take symmetrical action, and that's the way they view it is that they were delayed in taking this action", he added.
Last week, the US Congress passed a bill to toughen the unilateral US sanctions against Russia, Iran, and North Korea.
Kremlin spokesman, Dmitry Peskov said it is important that the USA president is thinking about the current situation and prospects for bilateral relations, but his intention to sign the sanctions bill into law contradicts the building of ties.More news: Government pledges €78m to help attract European Medicines Agency to Dublin
In another sign of US concern about the North, the Trump administration published a notice Wednesday in the Federal Register detailing a new ban on Americans traveling to North Korea.
The secretary of state said the administration has been attempting to exert "peaceful pressure" on North Korea, "because the options available to us are limited, particularly if we think we are operating under a short period of time".
Tillerson added that Trump will most likely sign the bill, adding however, that Washington will nevertheless try to restore relations with Moscow. "Does it make our life more hard?"
The Russian Foreign Ministry said if Washington takes new unilateral measures to reduce the number of Russian diplomats in the United States, a symmetrical response would follow. "Of course it makes our life more hard".More news: Samsung and Anritsu claim 1.2 Gbps with 6 carrier aggregation
Secretary of State Rex Tillerson is sitting on almost $80 million set aside for the State Department to combat propaganda from Russian Federation and terrorists groups - and most of it will expire if he doesn't act soon.
"It's an agreement that should serve America's interests first and foremost, and if it doesn't serve that interest, then why would we maintain it?"
"Do we want to tear it up and walk away?" he said.
But one Tillerson aide, R.C. Hammond, suggested the department might also be hesitant about using the money for one of its intended purposes: Pushing back on the Kremlin.More news: US Officials Say North Korea Capable of Hitting US in 2018
Tillerson has not filled almost 200 senior posts in the department, having resisted putting many people in place while he carries out a State Department restructuring so he can fulfill Trump's request to slash $10 billion from its budget.