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North Korean Minister of Foreign Affairs Ri Yong Ho said that his country may consider a test of a hydrogen bomb in the Pacific Ocean, according to a report from South Korea's official news agency Yonhap.
Ri said the potential test of "the most powerful detonation of an H-bomb" would be one possible "highest-level" action against the U.S., according to the report.
He added that he didn't know what actions would be ordered by Kim Jong-un, Yonhap reported.
Ri's threat is significant because such a detonation would move North Korea's nuclear weapons activities beyond its borders for the first time. Japan, for example, lies between North Korea and the Pacific Ocean.
The communist dictatorship's previous nuclear tests have taken place in its isolated mountains.
Hydrogen bombs are more powerful by an order of magnitude than the atomic bombs that North Korea tested in previous years. The country claims that an atomic test it carried out early this month was an H-bomb.
Ri is in New York attending the United Nations General Assembly.
The dollar was fetching as much as 112.55 yen before the news, but fell as low as 111.95 yen afterward.
Japan's chief government spokesperson said that North Korea's remarks and behavior were provocative and unacceptable, Reuters reported.
Early Friday, Kim said that the president's remarks at the U.N. merit the "highest level of hard-line countermeasure in history." The dictator said he is "thinking hard" about what kind of reaction Trump could have possibly expected when he delivered those remarks.
"The mentally deranged behavior of the U.S. president openly expressing on the U.N. arena the unethical will to 'totally destroy' a sovereign state, beyond the boundary of threats of regime change or overturn of social system, makes even those with normal thinking faculty think about discretion and composure," Kim said in a statement circulated on state news agency KCNA.
Kim urged the president to "exercise prudence in selecting words" after Trump on Tuesday issued a harsh warning to Pyongyang. The president threatened to "destroy" the communist nation if it threatened the United States.
Pyongyang's response comes hours after Trump signed an executive order that aims to expand his authority to target people and institutions doing business with North Korea. The measure seeks to cut off North Korea's access to funding and deter its nuclear and missile programs.
In recent weeks, North Korea has tested ballistic missiles and an apparent hydrogen bomb in the face of international economic sanctions and warnings. Last week, the U.N. unanimously passed fresh measures to punish the isolated nation economically, with the support of China and Russia.
—CNBC's Ted Kemp and Jacob Pramuk contributed to this article.