WASHINGTON (REUTERS) - US President Donald Trump said on Monday (July 22) his administration had very positive correspondence recently with North Korea, but the two sides have yet to set a time to restart talks aimed at ending Pyongyang's nuclear programme.

Asked at the White House if a new round of talks had been scheduled with North Korea, Trump said: "No, we just have a very good relationship and probably they would like to meet, and we'll see what happens.

"There was a little correspondence recently. We had very positive correspondence with North Korea. Again there's no nuclear testing, there's no missile testing, there's no nothing.

"I think we will, yeah, at a certain point... When they're ready, we'll be ready," Trump said.

Trump did not respond to questions about whether the correspondence was between and him and North Korean leader Kim Jong Un.

North Korea warned last week that if the United States broke a pledge not to hold military exercises with South Korea, it could put the nuclear talks - and its freeze in nuclear and missile testing in place since 2017 - at risk.

Trump had appeared to revitalise efforts to persuade North Korea to give up its nuclear weapons when he met Kim on the border between the Koreas last month and said they had agreed to resume working-level talks stalled since their failed summit in Hanoi in February.

US Secretary of State Mike Pompeo said at the time the talks would likely happen "sometime in July... probably in the next two or three weeks," but dates have yet to be announced and North Korean statements have raised doubts about when - and whether - they will go ahead.

Pompeo last week rejected the charge that military exercises would breach any agreement between Trump and Kim. And a top South Korean official said a US-South Korean military exercise would go ahead next month.

Pompeo told CBS in an interview on Monday he hoped the talks with North Korea would begin "soon."

He told Fox and Friends the State Department had "a number of conversations with the North Koreans" and that Kim had committed "getting our teams back to the negotiating table."

"I hope that we will," Pompeo said, adding: "I hope when they show up they take a position that's different."

Pompeo reiterated Kim had committed to denuclearise in the first summit with Trump in Singapore last year.

"It's time to begin to deliver on that," he said.

The Hanoi summit collapsed after US demands for North Korea's complete denuclearisation and North Korea's demands for relief from punishing sanctions.

While Trump's latest meeting with Kim demonstrated a rapport between the leaders, the two sides appear no closer to narrowing their differences. They have yet to agree on a common definition of denuclearisation, which North Korea has taken to include removal of the US nuclear umbrella protecting Japan and South Korea.

Pompeo said this month he hoped both sides could "be a little more creative" when they meet again.