Ri told the United Nations General Assembly earlier on Saturday that targeting the US mainland with its rockets was inevitable after "Mr Evil President" Trump called Pyongyang's leader "rocket man."
"Just heard Foreign Minister of North Korea speak at UN If he echoes thoughts of Little Rocket Man, they won't be around much longer!" Trump tweeted.
Trump and Kim have traded increasingly threatening and personal insults as Pyongyang races towards its goal of developing a nuclear-tipped missile capable of reaching the United States—something Trump has vowed to prevent.
In an unprecedented direct statement on Friday, Kim described Trump as a "mentally deranged US dotard" whom he would tame with fire. His comments came after Trump threatened in his maiden UN address on Thursday to "totally destroy" the country of 26 million people.
It was not clear from Trump's latest tweet if he was referring to Ri and Kim, or North Korea more broadly.
North Korea conducted its sixth and most powerful nuclear bomb test on September 3, prompting another round of UN sanctions. Pyongyang said on Friday it might test a hydrogen bomb over the Pacific Ocean.
"It is only a forlorn hope to consider any chance that the DPRK (North Korea) would be shaken an inch or change its stance due to the harsher sanctions by the hostile forces," Ri told the UN General Assembly on Saturday.
US Air Force B-1B Lancer bombers escorted by fighters flew in international airspace over waters east of North Korea on Saturday in a show of force the Pentagon said indicated the range of military options available to Trump.