US bombers have flown close to North Korea's east coast to demonstrate the military options available to defeat any threat, the Pentagon has said.
It said the flight was the farthest north of the demilitarised zone between the Koreas that any US fighter jet or bomber had flown in the 21st Century.
Tensions have risen recently over Pyongyang's nuclear programme.
At the UN, North Korea's foreign minister said US President Donald Trump was on a "suicide mission".
Ri Yong-ho's comments to the General Assembly mimicked Trump's remarks at the UN on Tuesday, when he called North Korean leader Kim Jong-un a "rocket man on a suicide mission".
Ri added that "insults" by Trump - who was, he said, "mentally deranged and full of megalomania" - were an "irreversible mistake making it inevitable" that North Korean rockets would hit the US mainland.
Trump, the foreign minister said, would "pay dearly" for his speech, in which he also said he would "totally destroy" North Korea if the US was forced to defend itself or its allies.
The US president responded to the speech on Twitter by saying Ri and Kim "won't be around much longer" if they continue their rhetoric.
Shortly before his address, the Pentagon announced that the show of force underscored "the seriousness" with which the US took North Korea's "reckless" behaviour, calling the country's weapons programme a "grave threat".
"This mission is a demonstration of US resolve and a clear message that the president has many military options to defeat any threat," it said in a statement.
"We are prepared to use the full range of military capabilities to defend the US homeland and our allies."
US Air Force B-1B Lancer bombers from Guam, escorted by Air Force F-15C Eagle fighters from Okinawa, Japan, flew in international airspace, the Pentagon added.
The flight follows a week of heated rhetoric between the leaders of both countries - after Trump's comments, Kim called him "mentally deranged" and "a dotard".
Ri did not comment on the Pentagon's announcement.
North Korea has refused to stop its missile and nuclear tests, despite successive rounds of UN sanctions. Its leaders say nuclear capabilities are its only deterrent against an outside world seeking to destroy it.
After the North's latest and most powerful nuclear test earlier this month, the UN Security Council approved new sanctions on the country.
But speaking at the UN, Ri repeated that the restrictions would not make the country stop its nuclear development.