Trump spoke Wednesday with South Korean President Moon Jae-in, and the Blue House readout of the call said the USA president promised he wouldn't attack North Korea while the two Asian nations hold talks.
"I probably have a very good relationship with Kim Jong-un", Mr. Trump told The Wall Street Journal in an interview. "I think you people are surprised".
Asked if he had spoken with Kim, Trump was evasive: "I'm not saying I have or haven't". I'm not saying I have or haven't.
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Russian Federation and China both advocate for a freeze-for-freeze plan that would see North Korea halt its testing of ballistic missiles and nuclear devices in return for The U.S.' freezing of joint military exercises.
The president said the USA was open to talks with North Korea under the right circumstances.
Direct talks between the USA president and Kim would be unprecedented.
Trump has mocked Kim's weight and called him "little rocket man" in a speech to the United Nations General Assembly.
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The North Korean leader claimed that he has a button on his desk to order a nuclear strike against the US, but for Kim to field a reliable nuclear deterrent against the USA and its allies, additional weapons testing will be undoubtedly be required.
But Pyongyang - which boycotted the 1988 Summer Olympics in Seoul - agreed Tuesday to send athletes and officials to the Games as the North and South held their first formal talks in two years at Panmunjom in the Demilitarised Zone.
The U.S. has not had formal negotiations with North Korea on its nuclear program since 2012.
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The 36-year-old took her time heading into the school, stopping to chat to the waiting students lined up outside to greet the royal visitor.