US President Donald Trump has said it was unclear if his planned summit with North Korean leader Kim Jong Un would still go forward and said he would continue to insist on denuclearisation of the Korean Peninsula.

It comes after North Korea threatened to cancel the summit if Washington presses ahead with its key demand for Pyongyang to unilaterally give up its nuclear arsenal.

The summit between both leaders is due to take place in Singapore on 12 June. 

"We'll have to see," Mr Trump told reporters in the Oval Office when asked if the summit was still on.

"No decision, we haven't been notified at all ... We haven't seen anything, we haven't heard anything," he said.

A statement carried on North Korea's official state news agency said if the Trump administration "unilaterally demands we give up nuclear weapons we will no longer have an interest in talks".

Citing deputy minister of foreign affairs Kim Kye Gwan, the news agency also said the fate of the US-North Korea summit, as well as bilateral relations, "would be clear" if Washington speaks of a Libya-style denuclearisation for the North.

The statement added Mr Trump would remain as a "failed president" if he follows in the steps of his predecessors.

The US is pressing North Korea for complete, verifiable and irreversible denuclearisation, but so far the North has not given any public indication of what concessions it is offering.

At a summit with the South's President Moon Jae-in last month, Mr Kim reaffirmed his commitment to the denuclearisation of the Korean peninsula.

But the phrase is a diplomatic euphemism open to interpretation on both sides.

"We already expressed our willingness for a denuclearised Korean peninsula and repeatedly declared that the US must end its hostile DPRK policy and nuclear threats as preconditions," the deputy foreign minister said.

In the past, North Korea has demanded the withdrawal of the US troops stationed in the South to protect it from its neighbour, and an end to the United States' nuclear umbrella over its security ally.

The North has long said it needs nuclear weapons to protect itself against a US invasion. 

Yesterday, North Korea abruptly cancelled high-level talks with South Korea, due to take place today, because of anger over its joint military exercises with the United States.