North Korean leader Kim Jong-un has praised US President Donald Trump and expressed satisfaction over the progress of talks between the two countries about a second summit, according to state media in Pyongyang.

Kim said he would trust Trump's approach, the North's official KCNA news agency reported on Thursday, weeks after the North Korean leader warned his country could seek a "new path" if the United States continued sanctions and diplomatic pressure.

"Kim Jong-un said that we will believe in President Trump's positive way of thinking, wait with patience and in good faith and, together with the US, advance step by step towards the goal to be reached by the two countries," KCNA said.

The report said Kim expressed "large satisfaction" at receiving a "great" letter from Trump and a briefing about the results of the negotiations from the North Korean delegation that visited Washington last week, but did not elaborate.

Kim ordered working-level preparations for the second North Korea-US summit to be done well, KCNA said. The White House said last week a second Trump-Kim summit would be held in late February but did not say where.

The two leaders met for the first time in a landmark summit in Singapore last June, which produced a vague promise to work towards the complete denuclearisation of the Korean peninsula. Progress since then has been patchy.

Kim has indicated to South Korean President Moon Jae-in he would undertake a "groundbreaking" denuclearisation measure, South Korean newspaper Dong-a Ilbo reported on Thursday.

The newspaper, citing an unidentified source with direct knowledge of the US-North Korea situation, said the same had been made clear to Trump during senior North Korean official Kim Yong-chol's Washington visit last week.

North Korea has hinted, for example, at the possibility of agreeing to the US demand for verification of denuclearisation efforts before it discards its Yongbyon nuclear facilities.

In turn, the US has mentioned potential measures such as easing limits on oil imports, a conditional restart of the Kaesong Industrial Zone in North Korea, and opening a liaison office in Pyongyang, Dong-a reported.

Agencies