The US will not allow the nuclear-armed North Korean regime to hold the world hostage, he said.
"A sustained cessation of North Korea's threatening behaviour must occur before talks can begin. Apart from that step, there are no preconditions for talks, nor will we accept pre-conditions from North Korea or others," Tillerson said in his address to the Security Council on North Korea.
"We will continue to hold North Korea accountable for its reckless and threatening behavior today and in the future. We ask every nation here to join us in exerting sovereignty to protect all of our people," Tillerson said.
"For those nations who have not done so, or who have been slow to enforce Security Council resolutions, your hesitation calls into question whether your vote is a commitment to words only, but not actions," he said.
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Tillerson said after its ICBM launch on November 29, the North Korean government claimed that it now possessed the capability to strike any location in the continental US.
"North Korea's growing capabilities reflect a direct threat to our security and the security of the entire world. We do not regard this claim as an empty threat," he said.
Japan holds the rotating presidency of the Security Council for the month of December.
Earlier US President Donald Trump said that while China is helping the US on North Korea, Russia is not.
Trump spoke with his Russian counterpart Vladimir Putin a day earlier on North Korea.
"The primary point was to talk about North Korea, because we would love to have his help on North Korea. China's helping. Russia's not helping. We'd like to have Russia's help. Very important," Trump said.
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