A banner near the U.S. Embassy in Seoul on Friday shows images, from left, of North Korean leader Kim Jong Un, South Korean President Moon Jae-in and President Trump. (Lee Jin-Man/AP)

President Trump on Saturday invited North Korean leader Kim Jong Un to meet him in the Korean demilitarized zone when he visits the peninsula over the next two days, setting up a potential third summit, an offer a Kim aide called “interesting.”

Trump made the offer in a morning tweet ahead of a second day of meetings at the Group of 20 summit here.

“After some very important meetings, including my meeting with President Xi of China, I will be leaving Japan for South Korea (with President Moon),” Trump wrote. “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(?)!”

Trump elaborated on his tweet during a photo op in a meeting with Saudi Crown Prince Mohammed bin Salman at the G-20, saying he “put out a feeler” to Kim to see if he would like to meet.

“I just thought of it this morning,” Trump said, although rumors that the White House was trying to arrange a potential meeting had circulated for days in Washington and Seoul.

“I don’t know where he is right now; he may not be in North Korea,” Trump said. In fact, if Kim had left the North, Trump almost certainly would have learned of it in his daily classified national security briefing, not to mention news coverage.

“I said, ‘If Chairman Kim wants to meet, I’ll be at the border,’” Trump said. “We seem to get along very well. That’s a good thing, not a bad thing. For the stupid people who say, ‘Oh, he gets along,’ it’s good to get along because if I didn’t become president you’d be having a war right now with North Korea.”

In a statement reported by state media organization KCNA, a senior North Korean official called Trump’s invitation an “interesting suggestion” but added that Pyongyang had not received an “official proposal.”

If the meeting takes place “on the dividing line, as intended by President Trump, it would serve as another meaningful occasion in further deepening the personal relations between the two leaders and advancing the bilateral relations,” said Choe Son Hui, North Korea’s first foreign vice minister.

White House aides have reportedly been working to arrange a visit for Trump to the DMZ, the heavily fortified area along the 38th parallel that has divided North and South Korea since the armistice that ended combat in the Korean War in 1953.

Past presidents have made the trip to talk to U.S. troops and peer through binoculars into enemy territory. Trump attempted to visit during a trip to Korea in November 2017, but the plan was aborted after Marine One encountered bad weather, forcing it to return to Seoul.

A senior administration official, briefing reporters ahead of Trump’s trip to Asia, indicated that no meeting between him and Kim was on the schedule.

“There are no plans for the meeting that you just mentioned,” the official, who was not authorized to speak on the record, told reporters. “The president is there to see President Moon. Of course, they’re going to talk about North Korea and they’re going to talk about the U.S.-South Korea alliance. But, you know, they’ve got a lot of ground to cover in two days. And then he’s coming back to D.C.”

A meeting between the two leaders would typically require elaborate planning and heightened security, but officials at the DMZ are accustomed to setting up high-level visits. Presidents Barack Obama, George W. Bush and Bill Clinton visited, as have Vice President Pence and Secretary of State Mike Pompeo.

When the U.S. military learned that Trump would be returning to the Korean Peninsula, it began preparing options for him, said a U.S. defense official with knowledge of the planning, speaking on condition of anonymity due to the sensitivity of the issue. The most likely locations for visits were Osan Air Base and Camp Humphreys, considering they are larger than other U.S. bases in South Korea. Trump said he will make an address to U.S. troops while he is in South Korea.

Military officials also anticipated that the president would be interested in going to the DMZ after the unsuccessful attempt in 2017.

“Pretty much every POTUS has been up there so we logically thought he’d want to go,” the defense official said.

A White House team on the ground set up plans with involvement by South Korean officials, the State Department and the Defense Department. A military “quick-reaction force” is prepared in case there is any kind of security emergency, the defense official said.

South Korean President Moon Jae-in met with Kim at the Joint Security Area in the DMZ in early 2018 and both leaders stepped over the border in a symbolic moment. It was a summit that paved the way from Trump’s first meeting with the North Korean leader in Singapore in June 2018.

A different U.S. official with knowledge of the planning said that arrangements had been made for Trump to visit Observation Post Ouelette, where other presidents have peered through binoculars into North Korea.

For Trump to change plans and visit the Joint Security Area right along the border would be “a big deal,” this official said.

“Until today, no one had been talking about POTUS going to JSA,” said the official, who spoke on the condition of anonymity to discuss private planning.

“In Seoul, the offer took a lot of people, in and out of government, by surprise,” said Richard Fontaine, the chief executive of the Center for a New American Security who visited South Korea this week. “As recently as today, the general expectation was that a third meeting would have to await some progress at the working level on denuclearization negotiations. Moon is likely to welcome this, seeing it as a jump-start to stalled diplomacy. The conservatives will likely see it as a further reward to Pyongyang in the absence of progress.”

The Korean Blue House issued a tweet reporting that Trump spoke briefly with Moon and asked if he had seen the tweet. Moon replied that he had seen it and told Trump: “Let’s try to doing it together.”

During his remarks Saturday, Trump marveled at the DMZ and seemed to envy at how secure the border is between the North and South.

“When you talk about a wall, talk about a border, that’s what they call a border,” said Trump, who is trying to build a wall along the U.S. southern border with Mexico. “Nobody goes through that border. That’s what’s called a real border.”

Trump and Kim held a second summit in Hanoi in February, but talks collapsed after the two sides failed to bridge divides over North Korea’s nuclear weapons and ballistic missile programs. Pyongyang offered to shutter one nuclear facility in exchange for the lifting of some economic sanctions, while the Trump administration demanded that the North relinquish its entire program.

Since then, there has been little communication, except for an exchange of personal letters between Kim and Trump over the past several weeks.

Trump is scheduled to depart Osaka on Saturday evening for Seoul, where he will spend one night before returning to Washington.

Dan Lamothe contributed to this report.