The top US commander in the Pacific warned Tuesday he must "imagine the unimaginable" in responding to the threat posed by the North Korea's nuclear weapons programme.

Admiral Harry Harris, head of the US Pacific Command, made clear that while diplomacy remains the preferred option in pressing Pyongyang to abandon its atomic weapons programme, that approach is backed by "credible" military power.

"Many people have talked about military options being unimaginable regarding North Korea," Harris said at an annual forum in Singapore.

"Folks, I must imagine the unimaginable. And what is unimaginable to me are North Korean nuclear-tipped missiles delivered in Los Angeles, in Honolulu, in Seoul, in Tokyo, in Sydney, in Singapore," he said.

US President Donald Trump and Defense Secretary Jim Mattis "do not come to me and ask for diplomatic or economic solutions," he added, speaking at an event organised by the International Institute for Strategic Studies.

"They come to me and ask for hard power options and that's what I provide them."

Tensions over North Korea's weapons programme have soared in recent months, with Pyongyang launching a flurry of missiles and conducting its sixth and most powerful nuclear test.

Trump has engaged in an escalating war of words with the North's leader Kim Jong-Un, trading personal insults and threatening to "totally destroy" the country if it threatens the United States.

But US Secretary of State Rex Tillerson said Sunday that Trump wanted to avoid war, even though the president said on Twitter that Tillerson was "wasting his time" with diplomacy.

Harris declined to comment when asked if the US military options included a preemptive strike.

But he called Kim a "reckless dictator" and warned that "combining nuclear warheads with ballistic missiles in the hands of a volatile leader ... is a recipe for disaster."

North Korea on Monday told the United Nations that it will never negotiate the dismantling of its nuclear weapons unless the United States reverses its "hostile" policy.

The US and South Korea on Monday began a 10-day joint naval exercise in a fresh show of force against the North, with a US aircraft carrier and two US destroyers taking part.