President Donald Trump's address to the United Nations General Assembly last week was noted for its aggressiveness, bellicosity and emphasis on U.S. sovereignty over multilateralism. Whatever one thinks of that approach, that wasn't the most notable aspect. The speech appeared to make an open and outright threat to commit genocide: "The United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea."

Had Trump threatened to "totally destroy" that country's nuclear weapons capacity, its army, its government, or its physical infrastructure, the implications under international law would be different, but carrying out his threat "to totally destroy North Korea" would necessarily sow mass death among its population of over 25 million, in direct contravention of the 1948 United Nations Convention on the Prevention and Punishment of the Crime of Genocide. The Convention defines genocide as acts that are undertaken with the intent to destroy, "in whole or in part," a "national, ethnical, racial or religious group, as such." While simply threatening to commit genocide is not a clear violation of the Convention, conspiracy and public incitement to do so are. If Trump were to act on his threat, he will have signalled his intent in advance.

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Just as disturbingly, Kim Jong-un's regime in North Korea has made similar threats. Its Korea Asia-Pacific Peace Committee, which oversees North Korea's relations with the outside world, has asserted: "The four islands of the [Japanese] archipelago should be sunken into the sea by the nuclear bomb," adding that "Japan is no longer needed to exist near us." That statement came in response to the UN Security Council's unanimous vote in support of Resolution 2375, which had condemned Pyongyang's missile test and imposed sanctions on North Korea. The committee also singled out the United States for its leadership in drafting the resolution: "Let's reduce the US mainland into ashes and darkness. Let's vent our spite with mobilisation of all retaliation means which have been prepared." Both of these constitute clear threats of genocide.

Washington and Pyongyang are bound by international law, which explicitly includes the provisions of the Genocide Convention. It is unprecedented for a leader of a state that has signed the Convention, as the United States did in 1988, to mount a UN platform and apparently flout this core component of international criminal law. (As the United Nations created the Genocide Convention, the Security Council is also responsible for enforcing it.) It is likewise an egregious attack on the Convention, which North Korea signed in 1989, to threaten sovereign nations and their people so seemingly casually.

If, heaven forbid, armed conflict actually erupts, both leaders have already announced the standard against which they should be judged. If they carry out their threats, we do not have to work hard to compare them to the 20th century's greatest monsters. They declared the likeness themselves.

Ben Kiernan, founding director of Yale's Genocide Studies Program, is the author of "Blood and Soil: A World History of Genocide and Extermination from Sparta to Darfur." Simon is the director of the Genocide Studies Program at Yale University. David Simon is the director of the Genocide Studies Program at Yale University.