The US President had recently expressed disappointment that Beijing had not applied as much pressure as he would like or caused a change in North Korea's behaviour. We do not seek a collapse of the regime.
But Tillerson said the USA does not think productive talks would result if North Korea came with the intention of maintaining their nuclear weapons.
Tillerson made the remarks at the US State Department on Tuesday after North Korea tested its second intercontinental ballistic missile (ICBM) on July 28, the Washington Post reported.
But he sought to reassure the isolated authoritarian regime that it does not need a nuclear arsenal to defend itself from a USA attack. "We're not your threat, but you are presenting an unacceptable threat to us, and we have to respond". "We do not seek an excuse to send our military north of the 38th parallel", Tillerson said.
In apparent attempt to reach out to supreme leader Kim Jong-un yesterday, he said: "We're not your enemy".
Pakistan to elect new prime minister on Tuesday
He nominated former Oil Minister Shahid Khaqan Abbasi as an interim prime minister. No civilian prime minister in Pakistan has ever completed a full term in office.
But here too, Tillerson was more diplomatic. "And we hope that at some point they will begin to understand that and we would like to sit and have a dialogue with them".
"This is going to be a continued effort to put ever greater pressure on the North Korean regime because our other options, obviously, are not particularly attractive", he said.
Tillerson's views on North Korea and its close ally, China, is in sharp contrast to the United States envoy to the UN, Nikki Haley, who on Sunday asked Beijing to decide on tougher UN sanctions on North Korea over its two long-range missile tests last month.
Last week, Kim boasted that North Korea could attack any target in the USA after carrying out its latest intercontinental ballistic missile (ICBM) test.
Republican foreign policy hawk Senator Lindsey Graham said Trump is ready to launch a devastating military strike if diplomacy fails to stop the nuclear missile threat.
U.S. officials have steadily condemned North Korea's missile tests, which are a violation of global law.