Trump called Kim a "madman" on Friday, a day after Kim dubbed him a "mentally deranged USA dotard". I don't want war.
"But the North is leaving too little room for the U.S. to do so with the latest series of threats and provocations", he said.
The flight underscored "the seriousness with which we take North Korea's reckless behaviour", the Pentagon said.
The KCNA said other party and military officials made speeches at the rally.
He told world leaders he was putting America first.
The film issues a stern warning to the United States, with subtitles stating: "Should F-35, B-1B and the Carl Vinson lead the USA attack, they will head to the grave in that order". Treasury Secretary Steven Mnuchin repeated the insistence that all options, including military force, remain on the table.
He added, "I'm going to handle it because we have to handle it", warning of North Korea's threats of "a massive weapon exploding over... the Pacific Ocean, which causes tremendous, tremendous calamity".
North Korea's foreign minister brought a dictionary full of insults for Trump when he addressed the U.N. General Assembly on Saturday. "This requires the worldwide community to work together", Xi said.
"North Korea's nuclear weapons and missile development is a grave threat to peace and security in our world and it is unacceptable that others financially support this criminal, rogue regime", Mr Trump said as he joined Japanese Prime Minister Shinzo Abe and South Korean President Moon Jae-in for a meeting in NY.
US President Donald Trump's war of words with North Korea is continuing to escalate.
North Korean Foreign Minister Ri Yong-ho, who had earlier compared Mr Trump's speech to "the sound of a barking dog", has warned that Pyongyang could test a hydrogen bomb in the Pacific Ocean in response to the USA president's threat.
Foreign Minister Ri Yong Ho, who took the General Assembly stage on Saturday, also said Trump's insults made plans to fire rockets at the USA mainland "inevitable".
Washington announced tougher restrictions Friday aimed at curbing North Korea's nuclear and ballistic missile program, building on tough new United Nations sanctions aimed at choking Pyongyang of cash.
On Twitter, Trump responded to Foreign Minister Ri Yong-ho's speech with yet another threat.
It was the farthest north of the Demilitarised Zone (DMZ) that United States fighters or bomber aircraft have ever flown this century.
Those new sanctions bar ships and aircraft from visiting the U.S. within 180 days of having gone to North Korea.
"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.
The fleet of B-1B Lancer bombers was escorted by the F-15C fighter jets over global waters on Saturday.
China wields the most influence on North Korea, providing an economic lifeline.
The regime said it was the successful launch of a hydrogen bomb mounted on an intercontinental ballistic missile. The reports revealed that the U.S. would have a hard time engaging and intercepting North Korean ballistic missiles.
The subtitle of the film says, "Should F-35, B-1B and the Carl Vinson lead the US attack, they will head to the grave in that order".