Referring to the series of weapons tests, Trump said, "North Korea is behaving badly and it's got to stop". On Sunday, Defense Secretary Jim Mattis said in a statement that the United States is prepared for "a massive military response" to any attacks from North Korea to it or one of its allies.
The Republican president said the US military "has never been stronger", but that "hopefully" Washington will not have to use it against Pyongyang.
The International community condemned North Korea for testing the hydrogen bomb on August 27, marking the sixth time the isolated state has tested a nuclear weapon.
The U.S. -drafted resolution, circulated to council members Wednesday and obtained by The Associated Press, would also prohibit North Korea from exporting textiles and ban all countries from hiring and paying workers from the northeast Asian nation-two key sources of foreign currency.
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At an emergency Security Council meeting last week, US Ambassador to the UN, Nikki Haley, announced that her delegation was circulating the draft resolution.
South Korea is planning to deploy additional launchers of a controversial US -built missile defense system, a further sign of escalating tensions and a diplomatic stalemate over North Korea's growing nuclear weapons program.
Later, a senior Trump administration official said that North Korea is a "global menace" and these latest provocations increase the worldwide communities resolve to isolate the North Korean regime through strict enforcement of existing United Nations security council resolutions and the imposition of new sanctions.
However, its continued efforts - including a test of a hydrogen bomb on September 3 - have irked allies such as China and Russian Federation and led to louder calls for tougher sanctions.
The President says he is had a "strong and frank" talk with his Chinese counterpart following Pyongyang's latest nuclear test.
"We support the Security Council in making further reactions and taking necessary measures", he said, adding "we hope to resolve this issue through dialogue and consultation".