Donald Trump is expecting to meet North Korean leader Kim Jong-un for the second time “quite soon.” The US president did not elaborate on a possible venue or date for such a meeting.

Details of Trump's second summit with Kim will be worked out in the immediate future, Trump told the media on Monday after a UN meeting on the Global Call for Action on the World Drug Problem.

"The relationships are very good with North Korea… [It] looks like we'll have a second summit quite soon. As you know, Kim Jong-un wrote a letter – a beautiful letter – asking for a second meeting and we will be doing that.”

READ MORE: US President Donald Trump says he's set to meet North Korean leader Kim Jong-un soon

The location of his next meeting with Kim has not yet been determined, but will likely take place at a different location than Singapore, Trump said.

The first historic meeting between the two leaders took place in Singapore in June. However, talks between Pyongyang and Washington have stalled since then. Last month, Trump canceled the planned visit of Secretary of State Mike Pompeo to Pyongyang, citing insufficient progress towards the denuclearization of the Korean Peninsula.

On Monday, the US leader seemed to change tone as he hailed "tremendous progress on North Korea."

Meanwhile, South and North Korea have been settling matters in relation to the peninsula on their own. Last week, the two Koreas made unprecedented steps towards reconciliation and denuclearization, signing a military agreement and a joint declaration. One of the most remarkable steps, later praised by Trump, was the North’s commitment to permanently shut down its Sohae Satellite Launching Station.

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