A statement by North Korea's official KCNA news agency issued on Saturday said the Trump administration "had better talk and act properly", if it did not want "the American empire to meet its tragic doom".
"I think it takes a combined message there for everyone to get effective movement out of the regime in North Korea".
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The U.S. "would suffer a shameful defeat and final doom if it persists in extreme military adventure, sanctions and pressure", said one North Korean official on Thursday.
See the president's full remarks in the video below.
Inflammatory rhetoric between the United States and North Korea over Pyongyang's nuclear programme soared to new heights this week when North Korea announced plans to fire rockets near Guam, a western Pacific island that is home to a U.S. military base and around 160,000 people.
A White House statement on the phone call did not mention the apparent plea to the U.S. president. The isolated nation, earlier this week, laid out a detailed plan to launch ballistic missiles into waters near Guam, a USA territory.
Long standing tensions between the country have been rising ever since North Korea tested two intercontinental missiles in July.
Last year, North Korea focused its provocative rhetoric on New York City, claiming it could "burn Manhattan down to ashes" after testing what it said was a hydrogen bomb.
The American people, Trump said, should be "very comfortable". "But we think lots of good things could happen".
The Hermit Kingdom's latest threat to launch a missile at US territory Guam has pushed the world closer to boiling point after US President Donald Trump warned of "fire and fury".