On Aug. 8, Trump threatened the regime with "fire and fury like the world has never seen", leading Kim to say he would consider sending missiles into the waters off the coast of Guam in "mid-August".
Trump fired back hours later. That might be a unusual thing that happens.
He also tweeted about meeting with Russian President Vladimir Putin at APEC and how they had "good discussions" on Syria and that he hopes that they can solve the North Korea crisis together. "But it is certainly a possibility", Trump said.
North Korea and its nuclear weapons program have plagued the USA for years.
Earlier this week the U.S. president said: "It makes sense for North Korea to come to the table and make a deal that is good for their people and for the world".
Trump and Kim have engaged in name-calling in recent months as tensions between the two countries increase and North Korea continues expanding its nuclear program.
Following his stop in South Korea, the President travelled on to China - North Korea's biggest ally and trading partner.
Shortly after that speech, North Korean officials told CNN, "We don't care about what that mad dog may utter", referring to Trump.
The Trump administration has said all military options remain on the table when dealing with the North Korean threat, but top USA officials have consistently emphasized the U.S.is pursuing a diplomatically led effort, including additional economic pressure.
Last month North Korea made threats to reduce the U.S. to "ashes and darkness" in response to sanctions imposed by the UN.
The president renewed his spat with North Korea as three US aircraft carriers were taking part in a military exercise in the Western Pacific in a show of strength to North Korea. It involves the USS Ronald Reagan, the USS Nimitz and the USS Theodore Roosevelt.
The strike force plans to conduct air defense drills, sea surveillance, defensive air combat training as well as other maneuvers.
In September Kim described Trump as a "mentally deranged US dotard" whom he would tame with fire.
Trump continued to push his harsh rhetoric for North Korea on Sunday, telling reporters that "the world has been provoked" by the rogue nation.
"And this artificial Democratic hit job gets in the way", Mr Trump said.