US President Donald Trump has invited North Korean leader Kim Jong-un to meet him at the fortified area that divides North and South Korea.
In what Mr Trump described as a spontaneous gesture, he said on Twitter he could "shake [Mr Kim's] hand and say hello" during his visit to South Korea.
The US president arrived in Seoul on Saturday to discuss the flagging North Korea denuclearisation talks.
The North described Mr Trump's offer as "very interesting".
If Mr Trump and Mr Kim were to see each other at the demilitarised zone (DMZ), it would be their third meeting in just over a year, and their first since a summit in Vietnam broke down in February.
After some very important meetings, including my meeting with President Xi of China, I will be leaving Japan for South Korea (with President Moon). While there, if Chairman Kim of North Korea sees this, I would meet him at the Border/DMZ just to shake his hand and say Hello(?)!— Donald J. Trump (@realDonaldTrump) June 28, 2019
Mr Trump - who is visiting South Korea after attending the G20 summit in Japan - conceded that the pair could see each other only "for two minutes", leading one analyst to dismiss the potential meeting as "pointless theatre".
However, despite the apparent lack of any diplomatic preparation, some have suggested another face-to-face meeting between the pair could help reset relations and set the scene for future talks.
South Korean President Moon Jae-in hosted Mr Trump at a presidential Blue House dinner on Saturday evening.
Mr Moon praised Mr Trump's offer to meet Mr Kim, saying if accomplished it would be a "historic moment", and "even if it doesn't happen, President Trump has shown his great goodwill towards Chairman Kim Jong-un, so it is a great accomplishment in itself".
Mr Trump said he and Mr Moon had "become friends in a great battle and a great struggle".
What reaction has there been?
A few hours after Mr Trump's offer, North Korea's first vice-minister for foreign affairs, Choe Son-hui, said in statement: "We see it as a very interesting suggestion, but we have not received an official proposal in this regard."
Such a meeting, the statement added, "would serve as another meaningful occasion in further deepening the personal relations between the two leaders and advancing the bilateral relations".
It remains unclear whether officials with Mr Trump were briefed in advance about his overture to the North Korean leader, and South Korea's presidency said nothing was yet confirmed.
But last week, a South Korean official said Mr Trump was considering a trip to the DMZ, prompting speculation a meeting with Mr Kim could be possible. Mr Trump attempted to make a surprise visit to the area in November 2017, but was forced to abandon the plans due to bad weather.
Will it, could it, might it just work?
This is the international edition of Donald Trump's reality TV style politics. First send out a tweet inviting the leader of one of the most secretive regimes in the world to come and "say hello". Then have the world watch and guess if Kim Jong-un will show up.
But will it, could it, might it just work? Mr Kim made a two day journey to Hanoi in February by train and came back empty handed. If he makes this trip, however short, he will want to know the meeting will definitely take place and that he has something to gain.
There have been no public working-level meetings between Pyongyang and Washington since the Vietnam summit, so it is not clear what this brief "hello" will achieve other than a meet and greet photo-op. But what a picture that would be.
Some analysts fear Mr Trump's style of politics is too frivolous for what is a serious issue and that the goal of denuclearisation is being shoved aside in favour of a good headline. But others believe that however unconventional, this meeting may at least kick-start more in-depth discussions in the future.
How are North Korea-US relations?
They have soured somewhat since Mr Trump and Mr Kim met in Hanoi, Vietnam. The summit - their second after Singapore in June 2018 - ended abruptly without agreement on North Korea's progress towards denuclearisation.
Mr Trump has repeatedly insisted that North Korea must dismantle its nuclear arsenal before economic sanctions can be lifted.
Since the Hanoi summit, North Korea has risked incurring the wrath of the Trump administration by testing several short-range missiles.
But Mr Trump, who once threatened North Korea with "fire and fury", has struck a more conciliatory tone recently, describing Mr Kim as a "very smart guy" and that he expected "a lot of good things" to come out of North Korea.
Last week, Mr Trump - who this month said North Korea under Mr Kim's leadership had "tremendous potential" - sent the North Korean leader a personal letter whose content Mr Kim praised as "excellent".
What is Mr Trump expected to discuss in Seoul?
The South Korean president's office said Mr Moon and Mr Trump would discuss "how to closely co-operate with each other to build lasting peace through complete denuclearisation of the Korean peninsula".
US special envoy on North Korea Stephen Biegun, who has been in Seoul recently for preparatory talks, was quoted as saying that the US was "ready to hold constructive discussions with North Korea".
Mr Moon, who has had two genial meetings with Mr Kim and was mediator for the first Trump-Kim summit, has made resolving the North Korean issue the focal point of his presidency.
Mr Trump will also be keen to demonstrate concrete progress as campaigning gets under way for the 2020 US elections.
The future of the US-South Korean post-war security alliance is also likely be on the agenda in Seoul. The US has about 30,000 personnel based in South Korea, and Mr Trump has repeatedly said he would like to scale back this deployment.
The two countries' militaries conduct annual war games which infuriate North Korea, but they have scaled them back since ties warmed last year.