US bombers escorted by fighter jets have flown close to North Korea's east coast, according to US officials, in a display of military strength after an escalating war of words between the two countries.

The Pentagon said Saturday's flight was the farthest north of the demilitarised zone separating North and South Korea that any US fighter jet or bomber has flown this century.

It said the operation over international waters showed the seriousness with which Washington took Pyongyang's "reckless behaviour", amid rising tensions over North Korea's nuclear tests.

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

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

Bellicose rhetoric

The B-1B Lancer bombers took off from Guam and the US Air Force F-15C Eagle fighter escorts came from Okinawa, Japan.

The flight came after days of heightened rhetoric between Washington and Pyongyang, with US President Donald Trump and North Korea's leader Kim Jong-un trading insults.

Trump called Kim a "madman" on Friday, a day after the North Korean leader dubbed him a "mentally deranged US dotard" in retaliation for the US president saying Washington would "totally destroy" the Asian country if it threatened the US or its allies.

Later on Saturday, North Korea's foreign minister said Trump's remarks against Pyongyang and Kim will make the US mainland an "inevitable" target for rocket attacks.

"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," Ri Yong-ho said at the United Nations General Assembly, an annual gathering of world leaders at the body's headquarters in New York.

Scott Snyder, director of the programme on US-Korea policy of the Council on Foreign Relations, said Washington's latest move was aimed at putting further pressure on Pyongyang.

"The growing intensity of activity is designed to send a message to Kim Jong-un that the US wants North Korea to turn in a different direction and that the US has the power to retaliate against him if he persists," he told Al Jazeera from Washington, DC.

"It is not clear Kim Jong-un is receiving that message."

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North Korea, a country of 26 million people, says it needs a strong nuclear deterrent to protect it from the US, and its government has made militarism a central part of its national ideology.

Pyongyang conducted its sixth and largest nuclear test on September 3 and has launched dozens of missiles this year, and has threatened to test a hydrogen bomb over the Pacific.

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