US President Donald Trump has made new threats against North Korea in response to the country's foreign minister's fiery speech at the UN on Saturday.
Ri Yong-ho described Mr Trump as a "mentally deranged person full of megalomania" on a "suicide mission".
The US president responded by saying Mr Ri and North Korean leader Kim Jong-un "won't be around much longer" if they continue their rhetoric.
The fresh insults came as US bombers flew close to North Korea's east coast.
The Pentagon said the aim was to demonstrate the military options available to the US to defeat any threat.
Just heard Foreign Minister of North Korea speak at U.N. If he echoes thoughts of Little Rocket Man, they won't be around much longer!— Donald J. Trump (@realDonaldTrump) September 24, 2017
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.
Despite weeks of angry words, experts have played down the risk of direct conflict between the two. However, there are concerns that the escalating rhetoric could lead to one side misinterpreting the other, with dangerous consequences.
Ri Yong-ho's comments to the General Assembly on Saturday mimicked Mr Trump's remarks at the UN on Tuesday, when he called North Korean leader Kim Jong-un a "rocket man on a suicide mission".
Mr Ri said that "insults" by Mr Trump were an "irreversible mistake making it inevitable" that North Korean rockets would hit the US mainland.
The US president, 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.
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 Mr Trump's comments, Mr Kim called him "mentally deranged" and "a dotard".
Mr 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, Mr Ri repeated that the restrictions would not make the country stop its nuclear development.