According to Yonhap News Agency, Kang and Guterres met earlier in the day to discuss the escalation of tensions on the Korean peninsula, caused by an exchange of threats by North Korean leader Kim Jong-un and US President Donald Trump.
"The whole world should clearly remember it was the US who first declared war on our country", Foreign Minister Ri Yong Ho told reporters in NY.
This applied even when they were not in the North Korean airspace, the minister added.
"The question of who will be around much longer will be answered then".
Ri's remarks were the most direct and threatening so far since Trump gave a combative address to the General Assembly last week in which he threatened to "totally destroy" North Korea.
"In light of the declaration of war by Trump, all options will be on the operations table of the supreme leadership of the DPRK".
The U.S. and North Korea exchanged barbs during a tense week at the UN General Assembly (UNGA) beginning on September 19 with an inaugural speech to the body by Trump.
"Atrocious and stupid Trump, who has no political career, appearance befitting a politician, and elementary etiquette and morality as a human being, revealed the nature of a mad dog" in his threats at the United Nations, a commentary in North Korean state media argued.
The remarks from the rogue state's Foreign Minister is in reaction to comments made by the President of the U.S. in which he questioned how long the North Korean leadership would exist for. The second came after Ri delivered a hostile speech at the United Nations warning that a strike on the USA mainland is "inevitable" because of Trump's earlier statements.