In this handout image provided by South Korean Defense Ministry, U.S. Air Force B-1B Lancer bombers flying with F-35B fighter jets and South Korean Air Force F-15K fighter jets during a training at the Pilsung Firing Range on September 18, 2017 in Gangwon-do, South Korea. U.S. F-35B stealth jets and B-1B bombers flew near the Military Demarcation Line (MDL) for the first time since recent tension between U.S. and North Korea started raising.

North Korea said on Saturday targeting the U.S. mainland with its rockets was inevitable after "Mr. Evil President" Donald Trump called Pyongyang's leader "rocket man", further escalating rhetoric over the North's nuclear weapons and missile programs.

North Korean Foreign Minister Ri Yong Ho's remarks to the United Nations General Assembly came hours after U.S. Air Force B-1B Lancer bombers escorted by fighters flew in international airspace over waters east of North Korea, in a show of force the Pentagon said showed the range of military options available to Trump.

Ri's speech capped a week of rising tensions between Washington and Pyongyang, with Trump and North Korean leader Kim Jong Un trading insults. Trump called Kim a "madman" on Friday, a day after Kim dubbed him a "mentally deranged U.S. dotard."

On Saturday, the mudslinging continued with Ri calling Trump "a mentally deranged person full of megalomania and complacency" who is trying to turn the United Nations into a "gangsters' nest". Ri said Trump himself was on a "suicide mission" after the U.S. president had said Kim was on such a mission.

"'President Evil' is holding the seat of the U.S. President," Ri said, warning that Pyongyang was ready to defend itself if the United States showed any sign of conducting a "decapitating operation on our headquarters or military attack against our country."

"Now we are finally only a few steps away from the final gate of completion of the state nuclear force," Ri told the annual gathering of world leaders.

He said sanctions would have no effect on Pyongyang's resolve to develop its nuclear weapons, with the ultimate goal being "balance of power with the U.S."

Trump announced new U.S. sanctions on Thursday that he said allow targeting of companies and institutions that finance and facilitate trade with North Korea.

Earlier this month the U.N. Security Council unanimously adopted its ninth round of sanctions on Pyongyang to counter its nuclear and ballistic missiles programs.

The U.S. bombers' flight was the farthest north of the demilitarized zone separating North and South Korea that any U.S. fighter jet or bomber has flown in the 21st century, the Pentagon said.

"This mission is a demonstration of U.S. resolve and a clear message that the President has many military options to defeat any threat," said Pentagon spokeswoman Dana White.

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

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.

Earlier on Saturday, U.S. Air Force B-1B Lancer bombers escorted by fighter jets flew in international airspace over waters east of North Korea.

The Pentagon said the maneuver was a show of force that demonstrated the range of military options available to the president.

The flight, which was disclosed shortly before North Korea's foreign minister was due to address the United Nations, was the farthest north of the demilitarized zone separating North and South Korea that any U.S. fighter jet or bomber has flown in the 21st century, the Pentagon said.

"This mission is a demonstration of U.S. 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 weapons program "a grave threat."

"We are prepared to use the full range of military capabilities to defend the U.S. homeland and our allies," White said.