Trump had said he would "love to meet" Kim during his Asia trip, which would have been their first meeting since the US leader's previous term in the White House.

North Korea has not responded publicly to the invitation.

Just hours before Trump began a visit to South Korea, Pyongyang announced North Korea test-fired cruise missiles off its western coast in a message to Pyongyang "enemies".

"I know Kim Jong Un very well... we really weren't able to work out timing," Trump said.

Trump added he would aim to "straighten out" tensions between North Korea and South Korea as he met Seoul's President Lee Jae Myung for a summit.

Lee, whose country remains technically at war with North Korea, hailed Trump's invitation to Kim, saying it had created "significant sense of warmth and peace on the Korean peninsula".

Trump said earlier on Wednesday he expected to meet with Kim in the "not too distant future".

"At some point, we'll be involved with North Korea. I think they'd like to, and I'd like to," Trump told reporters on Air Force One.

Kim met Trump three times for high-profile summits during the US leader's first term.

The duo's last and impromptu meeting took place at Panmunjom, in the DMZ which separates the two Koreas.

It was hastily arranged after Trump extended an invitation to Kim on Twitter a day prior.

That event saw the two leaders shake hands over the concrete slabs dividing North and South before Trump walked a few paces into Pyongyang's territory -- becoming the first US president ever to set foot on North Korean soil.

But talks collapsed over just how much of its nuclear arsenal the North was willing to give up and what Pyongyang would get in return.

Since then, North Korea has repeatedly declared itself an "irreversible" nuclear state.