North Korea's Foreign Minister has told the United Nations it is "inevitable" Pyongyang will target the US mainland with its rockets, after President Donald Trump made fiery comments about the rogue state's leader.

Key points: North Korea calls Donald Trump 'mentally deranged person full of megalomania'

North Korea calls Donald Trump 'mentally deranged person full of megalomania' US bombers fly over waters east of North Korea in show of force

US bombers fly over waters east of North Korea in show of force Pyongyang "only few steps away" from completing its nuclear force, Foreign Minister says

Ri Yong-ho told the UN General Assembly Mr Trump was on a "suicide mission" and had made "our rockets' visit to the entire US mainland inevitable", by calling North Korean leader Kim Jong-un "rocket man on a suicide mission" in his own address days earlier.

Mr Ri said Mr Trump was a "mentally deranged person full of megalomania and complacency", who is "chastised even by the American people as 'Commander in Grief, 'Lying King', 'President Evil'.

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"The respected supreme leader Comrade Kim Jong-un stated: 'As a man representing the DPRK and on behalf of the dignity and honour of my state and people and on my own, I will make the man holding the prerogative of the supreme command in the US pay dearly for his speech calling for totally destroying the DPRK'," Mr Ri said.

Mr Ri's speech capped a week of rising tensions between Washington and Pyongyang, with Mr Trump and Mr Kim trading insults.

In Mr Trump's first speech to the US General Assembly, he vowed to "totally destroy" North Korea unless is backs down from its weapons programs.

Donald Trump called Kim Jong-un a "suicidal rocket man" in his own UN address. ( Reuters: Aaron P. Bernstein )

Mr Trump called the leader of the north a "madman" on Friday, a day after Mr Kim dubbed him a "mentally deranged US dotard".

The UN speech came just hours after US Air Force bombers, escorted by fighter jets, flew in international airspace over waters east of North Korea.

The move was in a show of force and demonstrated the range of military options available to Mr Trump, the Pentagon said.

"Through such a prolonged and arduous struggle, now we are finally only a few steps away from the final gate of completion of the state nuclear force," Mr Ri told the annual gathering of world leaders for the United Nations General Assembly.

"It is only a forlorn hope to consider any chance that the DPRK (North Korea) would be shaken an inch or change its stance due to the harsher sanctions by the hostile forces."

The flight, which was disclosed shortly before Mr Ri was due to address the United Nations, was the farthest north of the demilitarised zone separating North and South Korea that any US fighter jet or bomber has flown in the 21st century, the Pentagon said.

"This mission is a demonstration of US resolve and a clear message that the President has many military options to defeat any threat," Pentagon spokeswoman Dana White said, calling North Korea's weapons program "a grave threat".

"We are prepared to use the full range of military capabilities to defend the US homeland and our allies."

Sorry, this video has expired Donald Trump warns United States will 'totally destroy' North Korea if threatened

North Korea has held a large anti-US rally in Pyongyang's Kim Il-Sung Square following the exchanges between Mr Trump and Mr Kim.

A parade of marchers carried signs with slogans such as "decisive revenge" and "death to the American imperialists".

They shouted phrases such as "total destruction," according to the Korean Central News Agency, the state news service.

The crowd included workers, officials and students, KCNA said.

Tensions high on the Korean peninsula

North Koreans gathered at Kim Il Sung Square rallying against the United States. ( AP: Jon Chol-Jin )

North Korea has launched dozens of missiles this year, several flying over Japan, as it accelerates its program aimed at enabling it to target the United States with a nuclear-tipped missile.

The flight follows a week of heightened rhetoric from Washington and Pyongyang, with Mr Trump and Mr Kim trading insults.

Mr Trump called the North Korean leader a "madman" on Friday, a day after Kim dubbed him a "mentally deranged US dotard".

Pyongyang conducted its sixth and largest nuclear test on September 3, prompting a new round of UN sanctions.

US Air Force B-1B Lancer prepares to take off from Andersen AFB in Guam for a mission in international airspace over the waters east of North Korea. ( US Air Force: Sgt Joshua Smoot )

The Pentagon said the B-1B Lancer bombers involved in the fly over on Saturday (local time) came from Guam and the US Air Force F-15C Eagle fighter escorts came from Okinawa, Japan.

It said the operation showed the seriousness with which it took North Korea's "reckless behaviour".

The patrols came after officials and experts said a small earthquake near North Korea's nuclear test site on Saturday was probably not man-made, easing fears Pyongyang had exploded another nuclear bomb just weeks after its last one.

Mr Ri did not respond when asked by reporters whether North Korea had conducted a new nuclear test.

China's Earthquake Administration said the quake was not a nuclear explosion and had the characteristics of a natural tremor.

The US Geological Survey said it could not conclusively confirm whether the quake, which it measured at magnitude-3.5, was man-made or natural.

Reuters/AP