US President Donald Trump's insult, calling leader Kim Jong Un "rocket man", makes "our rocket's visit to the entire US mainland inevitable all the more", North Korea's foreign minister said.
Ri Yong Ho called the US leader "a mentally deranged person full of megalomania and complacency" with his finger on the "nuclear button" and declared: "None other than Trump himself is on a suicide mission."
He told world leaders on Saturday: "In case innocent lives of the US are lost because of this suicide attack, Trump will be held totally responsible."
Mr Ri's highly anticipated speech to the General Assembly's annual ministerial meeting fuelled the fiery rhetoric between the US president and North Korea's young leader.
Mr Trump threatened in his speech to the 193-member world body on Tuesday, to "totally destroy" the North if provoked.
Kim, in an unusual direct statement to the world, responded by pledging to take "highest-level" action against the United States.
Mr Ri suggested to reporters on Friday in New York that the country could conduct an atmospheric hydrogen bomb test to fulfil Kim's vows. But he did not make any mention of such a test on Saturday.
Mr Ri said: "Our national nuclear force is, to all intents and purposes, a war deterrent for putting an end to nuclear threat of the US and for preventing its military invasion, and our ultimate goal is to establish the balance of power with the US."
Mr Ri's comments came as the United States on Saturday flew bombers and fighter escorts to the furthest point north of the Demilitarised Zone by any such American aircraft this century, in a show of American military might.
The Pentagon said the mission showed how seriously President Donald Trump took North Korea's "reckless behaviour".
"This mission is a demonstration of US resolve and a clear message that the president has many military options to defeat any threat," Defence Department spokesman Dana White said in a statement.
"North Korea's weapons programme is a grave threat to the Asia-Pacific region and the entire international community.
"We are prepared to use the full range of military capabilities to defend the US homeland and our allies," Ms White said.
The Pentagon said B-1B bombers from Guam, along with F-15C Eagle fighter escorts from Okinawa, Japan, flew in international airspace over waters east of North Korea on Saturday.
The US characterised the flights as extending further north of the DMZ, which separates North and South Korea, than any US fighter or bomber had gone off the North Korean coast in the 21st century.
Mr Trump on Friday had renewed his rhetorical offensive against Kim.
"Kim Jong Un of North Korea, who is obviously a madman who doesn't mind starving or killing his people, will be tested like never before!" the president tweeted.
On Thursday, Mr Trump announced more economic sanctions against the impoverished and isolated country, targeting foreign companies that deal with the North.
"North Korea's nuclear weapons and missile development is a grave threat to peace and security in our world and it is unacceptable that others financially support this criminal, rogue regime," Mr Trump said as he joined Japanese Prime Minister Shinzo Abe and South Korean President Moon Jae-in for a meeting in New York.
B-1B bombers from Guam and F-15 fighter escorts from Okinawa in Japan have flown a mission in international airspace over the waters east of North Korea, the Pentagon said.
The US said it was the furthest north of the Demilitarised Zone that divides the Korean Peninsula that any American fighter or bomber has flown this century.
Defence Department spokesman Dana White said in a statement that the mission showed how seriously the US took what she called North Korea's "reckless behaviour".
The statement said the flights were a "demonstration of US resolve and a clear message" that President Donald Trump "has many military options to defeat any threat".
Ms White said "we are prepared to use the full range of military capabilities to defend the US homeland and our allies".
President Trump has threatened to "totally destroy" North Korea if the United States was forced to defend itself or its allies against a North Korean attack.
That led the North Korean leader, Kim Jong Un, to say Mr Trump would "pay dearly" for making such a threat.
Kim's foreign minister has said his country's response to Mr Trump "could be the most powerful detonation of an H-bomb in the Pacific".
A North Korean minister said US President Donald Trump's insult makes "our rocket's visit to the entire US mainland inevitable all the more".
The minister further described Trump as "a mentally deranged person full of megalomania" who is holding "the nuclear button".