Addressing the UN General Assembly last month, Trump mocked Kim Jong-un, saying: "Rocket man is on a suicide mission." He said that the US would destroy North Korea if it is forced to defend allies. In response, Pyongyang compared Trump's speech to a dog's bark!
Both countries have traditionally communicated through a diplomatic back-channel connecting the Department of State to Pyongyang's mission at the UN; Trump has restored these since entering the office.
These were originally set up to negotiate the release of several Americans imprisoned in North Korea.
While discussions on US-North Korea relations were reportedly conducted through these, it doesn't seem to have helped de-escalate the crisis.