A White House readout of the April 29 call characterized it as a "very friendly conversation." Days after the conversation, Trump said publicly that he would be "honored" to meet with Kim.
But in the call, Trump hinted at a possible dramatic escalation on the Korean Peninsula.
"We can't let a madman with nuclear weapons let on the loose like that. We have a lot of firepower, more than he has, times 20 — but we don't want to use it," the US leader said, citing "two nuclear submarines" the Pentagon sent to the area last month.
Transcribed by the Philippine government, the conversation was released by The Washington Post and The Intercept.
Trump also queried Duterte about whether he believed Kim was "stable or not stable." The Philippine leader responded that their North Korean counterpart's "mind is not working and he might just go crazy one moment."
Kim has a "dangerous toy in his hands that could create so much agony and suffering for all mankind," he added.
But Trump appeared reassured that North Korea's recent missile tests had failed, saying that "all his rockets are crashing. That's the good news."
Turning to China and its ability to counter the nuclear threat, Trump pressed Duterte to call Chinese President Xi Jinping to exert pressure.
"I hope China solves the problem. They really have the means because a great degree of their stuff come through China," Trump said, adding: "But if China doesn't do it, we will do it."
Duterte agreed. However, he cautioned, starkly, that "the other option is a nuclear blast, which is not good for everybody."