The US Secretary of State said relations between the two nuclear and economic superpowers has reached "a pivot point" as tensions over global affairs escalate. "We do not seek regime change".
The second test of an intercontinental ballistic missile (ICBM) on Friday, celebrated by North Korean leader Kim Jong-un, was the latest to be conducted in defiance of a United Nations ban. Relatives said they were told the 22-year-old University of Virginia student had been in a coma since shortly after he was sentenced to 15 years of hard labor in North Korea in March 2016.
"We don't think having a dialogue where the North Koreans come to the table assuming they're going to maintain their nuclear weapons is productive", he warned.
In June, US college student Otto Warmbier died following a prolonged detention in the country, provoking worldwide outrage and calls for action in congress. Warmbier had traveled to North Korea through a commercial tour company and was arrested for allegedly stealing a poster from his hotel.
But he sought to reassure the isolated regime that it does not need a nuclear arsenal to defend itself from a USA attack.
In a travel alert released Wednesday, the State Department urged all Americans now in North Korea to leave the country before the policy takes effect next month.
"We are not your enemy. but you are presenting an unacceptable threat to us, and we have to respond".
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According to a statement that appeared on the US Federal Register Wednesday, "The Department of State has determined that the serious risk to United States nationals of arrest and long-term detention represents imminent danger to the physical safety of United States nationals traveling to and within the Democratic People's Republic of Korea (DPRK)".
However, Mr Tillerson took a more diplomatic approach, saying that "only the North Koreans are to blame for this situation".
Meanwhile, a senior Republican senator said President Trump considered going to war with North Korea as an option.
Last week, Kim boasted that North Korea could attack any target in the USA after carrying out its latest intercontinental ballistic missile (ICBM) test. "The time for talk is over", she said.
"China has ways that they can influence and put pressure on the North Korean regime because of this significant economic relationship that no one else has", the Secretary of State argued.
In a separate development, Republican Senator Lindsey Graham said that Mr Trump told him that there would be a war between the two countries if Pyongyang continued with its aim to develop a missile programme with the U.S. in its range.