Kim said that Trump is "unfit to hold the prerogative of supreme command of a country".
His foreign minister, asked on a visit to NY to attend the U.N. General Assembly what the countermeasure would be, said his country may test a hydrogen bomb in the Pacific Ocean.
"A meeting can also be used to send a direct, tough message to the North Korean leadership about what the United States thinks and what it wants North Korea to do", Wit said.
"We have no idea about what actions could be taken as it will be ordered by leader Kim Jong-un".
Experts believe this is the first time a North Korean leader has made a direct address to an global audience.
North Korea fired a missile on Friday that flew over Hokkaido in northern Japan and landed far out into the Pacific Ocean, according to Japanese and South Korean officials, further ratcheting up tensions in the region.
"Our new executive order will cut off sources of revenue that fund North Korea's efforts to develop the deadliest weapons known to humankind", Trump said.
The Pentagon said the B-1B Lancer bombers came from Guam and the U.S. Air Force F-15C Eagle fighter escorts came from Okinawa, Japan. Also the epicenter was around where an artificial quake occurred on September 3, where North Korea conducted its sixth and most powerful nuclear test.
North Korea's weakest nuclear test, its first one, conducted in 2006, generated a magnitude 4.3 tremor.
"We can not deny the possibility it may fly over our country", he said.
South Korea's weather agency said a magnitude 3.2 earthquake was detected in North Korea on Saturday close to where the country recently conducted a nuclear test, but it assessed the quake as natural.
"North Korea's reckless pursuit of nuclear weapons and ballistic missiles threatens the entire world with unthinkable loss of human life ... no nation on Earth has an interest in seeing this band of criminals arm itself with a nuclear weapon and missiles", said Trump.
Abe said Japan, a treaty ally of the United States, consistently supported the US stance that "all options are on the table" in dealing with North Korea.
He also said he would "tame the mentally deranged USA dotard with fire".
North Korea's foreign minister has described as "the sound of a dog barking" President Donald Trump's threat to destroy his country.
The order boosts the US Treasury's ability to clamp down on individuals and companies that finance and facilitate trade with the reclusive state.
A ban on textile imports from the North will go into effect immediately, the statement said.
Mr Trump said "tolerance for this disgraceful practice must end now".