North Korea says firing its rockets at the US is now "inevitable" in response to US President Donald Trump calling Pyongyang's leader "rocket man".
North Korean Foreign Minister Ri Yong Ho's remarks before the United Nations General Assembly on Saturday came hours after US Air Force B-1B Lancer bombers escorted by fighter jets flew in international airspace over waters east of North Korea, in a show of force the Pentagon said demonstrated the range of military options available to Trump.
"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.
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"It is only a forlorn hope to consider any chance that the DPRK (Democratic People's Republic of Korea) would be shaken an inch or change its stance due to the harsher sanctions by the hostile forces," he said.
Mr Trump announced new US sanctions on Thursday targeting companies and institutions that finance and facilitate trade with North Korea. Earlier this month the UN Security Council unanimously adopted its ninth round of sanctions on Pyongyang to counter its nuclear and ballistic missiles programs.
Mr Ri, who said Pyongyang's ultimate goal was to establish a "balance of power with the US", retorted that Mr Trump himself was on a "suicide mission" after the US president said Kim Jong-un was on such a mission.
The US bombers' flight 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.
Mr Ri warned Pyongyang was ready to defend itself if the US showed any sign of conducting a "decapitating operation on our headquarters or military attack against our country".
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 Mr Kim dubbed him a "mentally deranged US dotard".
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.