Donald Trump has proposed a meeting with the North Korean leader, Kim Jong-un, in the demilitarized zone (DMZ) that divides the Korean peninsula between north and south.
"The fundamental problem - no working-level meetings and no basic change in at least the United States negotiating position - means that any meeting right now is just pointless theatre", Vipin Narang, an MIT professor of political science, said on Twitter.
The details haven't been revealed, . but the assumption is they meant cooperation on restarting nuclear talks with North Korean leader Kim Jong-un.
"I can tell you every - it seemed every week somebody was calling me to say, 'Missiles are being shot over Japan, '" he said.
Violence was more common in the Cold War, but a 2015 land mine blast blamed on North Korea maimed two South Korean soldiers and pushed the rival Koreas to the brink of an armed conflict.
Trump called Kim's letter, which included birthday wishes for himself, 'beautiful'.
Mr Trump wanted to visit the DMZ on a 2017 visit to South Korea but he was forced to put off the plan because of bad weather.
"There's no change in our position that we want North Korean-U.S. dialogue to resume", presidential spokeswoman Ko Min-jung said.
White House advisers Ivanka Trump and Jared Kushner also took part in the dinner, along with Secretary of State Mike Pompeo and Secretary of the Treasury Steven Mnuchin, held at the Sangchunjae pavilion, a handsome structure modeled after a traditional Korean house, or hanok.
In a rally organized by supporters of former conservative President Park Geun-hye, a participant wearing a Trump mask went onto a makeshift stage set up in front of Deoksu Palace and sang the national anthem of Korea.
Before that, the most famous incident at Panmunjom happened in 1976, when axe-wielding North Korean soldiers killed two USA officers sent out to trim a tree that obstructed the view from a checkpoint.
Trump and Kim last met in Vietnam in February, but that summit collapsed with no progress.
Her comments suggested that North Korea is willing to accept Trump's idea if it gets a formal US offer for the meeting, according to some observers in Seoul.
North Korea has been insisting on immediate relief from biting global sanctions before it takes any additional steps towards nuclear disarmament - a demand that has been balked at by Washington.
On Saturday, the USA president said he wanted to go and inspect the heavily-fortified area to see what a "real border" looks like.
"If he's there, we'll see each other for two minutes, that's all we can, but that will be fine", he said, adding he and Kim "get along very well".
Kim and Trump also exchanged personal letters earlier this month, fueling anticipation of a revival of talks.
Mr Moon, who has had two genial meetings with Mr Kim, has made resolving the North Korean issue the focal point of his presidency.
The visit comes days after Trump pulled back from the brink of armed conflict with Iran, and as he looks to de-escalate a year-long trade war with China.