The president is set to address the United Nations General Assembly.
Experts believe that backing North Korea into a corner could have unintended consequences.
Trump's threat to cut trade with North Korea's trade partners could be bad for the U.S. economy, experts warn.
Asked about Trump's latest comments, Secretary of Defense Jim Mattis instead emphasized the importance of diplomatic efforts.
The president invited the global community to unite in condemnation of the country's latest missile test.
The U.S. ambassador to the U.N., Nikki Haley, said the "world is on notice" after North Korea's latest missile test.
The U.N. ambassador tweeted after North Korea's intercontinental ballistic missile test on Monday.
The U.S. ambassador to the United Nations and the Secretary of defense each credit the president's "pay a price" threat, but did not offer direct evidence.
Nikki Haley spoke out against same-sex marriage when she was governor of South Carolina.
Two United Nations experts, including an American, were killed in Congo in March, but a local inquiry has been criticised.
She said she believed the arrest was leader Kim Jong Un "trying to really show his strength to the people of North Korea."
The U.N. deputy secretary-general says she and U.N. Secretary-General Antonio Guterres are concerned over the new administration's attitude toward fighting global warming.
Michael Sharp was abducted and killed in Congo while investigating a deadly insurgency.
President Joseph Kabila is due to step down when the next elections are held.
If Nikki Haley cannot reach agreement with Russia and China, then Russia's Deputy U.N. Ambassador Petr Iliichev said Moscow would call for a rare procedural vote to block the move.
Haley said there's "no love" between the U.S. and Russia.
Secretary of State Rex Tillerson and U.S. Ambassador to the U.N. Nikki Haley said the U.S. was no longer interested in pursuing regime change in Syria.
Haley outlined her agenda for the United Nations, including human rights and peacekeeping reform.
It is impossible to make America first by treating the world last.
North Korea fired the missiles into the sea off Japan's coast in response to the annual U.S.-South Korea military drills, which Pyongyang sees as preparation for war.
Nikki Haley said Washington "will not hesitate to call out Russia" for transgressions.
Haley's comments came after Trump said on Wednesday that he was open to ideas beyond a two-state solution.