Mr Tillerson singled out China for having turned up the heat on Pyongyang, an approach which he said was starting to bear fruit.
Speaking at an event at Stanford University in California, Mr Tillerson said South Korean President Moon Jae-in had attributed North Korea’s recent willingness to talk to South Korea to the pain of sanctions.
He added he was confident the intense pressure would eventually prompt North Korea to the negotiating table in order to discuss the future of its nuclear and missile programmes.
Citing intelligence and anecdotal evidence from defectors, Mr Tillerson said: “We are getting a lot of evidence that these sanctions are really starting to hurt.”
He said: ”We have never had Chinese support for sanctions like we’re getting now. Russia’s a slightly different issue, but the Chinese have leaned in hard on the North Koreans.”
Speaking of the recent thawing in relations between North and South Korea, Mr Tillerson said he was supportive of the ongoing dialogue between the two nations, adding that it “may be their early effort to break the ice.”
Mr Tillerson also referred to a Japanese report that more than 100 North Korean fishing boats had drifted into its waters recently, and that two-thirds of those aboard had died.
He said: “What they learned is that they are being sent out in the winter time because there’s food shortages and they are being sent out to fish with inadequate fuel to get back.”
Chinese representatives did not attend the Vancouver meeting, where 20 nations agreed to step up sanctions pressure on North Korea, but Mr Tillerson stressed the importance of the role played by Beijing.
Speaking of North Korea’s much-ridiculed leader, Kim Jong-un, Mr Tillerson said: “He knows how to reach me, if he wants to talk. But he’s got to tell me he wants to talk. We’re not going to chase him.”
The US Secretary of State said he was confident the sides would eventually get to the negotiating table and warned he has “very, very strong military options standing behind me.”
The Trump administration has said repeatedly that all options are available, including military action, in forcing North Korea to give up development of nuclear missiles capable of reaching the US, although it prefers a diplomatic solution.