SEOUL — President Trump said North Korea was “very receptive” to his invitation to meet strongman Kim Jong-un on Sunday at the demilitarized zone that separates the Korean peninsula, upping the ante of a visit designed to strategize with South Korean allies.

“I understand that we may be meeting with Chairman Kim,” Mr. Trump said Saturday in a press conference closing the end of the G-20 summit in Japan. “So we’ll see.”

The president also said he’d be willing to take the symbolic step of crossing into North Korean territory if Mr. Kim can meet at the DMZ.

“Sure I would, I feel very comfortable doing that. I would have no problem,” he said.

Mr. Trump left Japan and landed at Osan Air Force in South Korea just after 7 p.m., local time. He went straight to Seoul for dinner with President Moon Jae-in at the presidential residence, or Blue House, ahead of further meetings Sunday.

The president told reporters that yes, North Korea responded to his DMZ invitation, but didn’t elaborate.

“Well, we’re going to see,” he said.

Mr. Trump said he isn’t looking for anything substantial from Mr. Kim — just a “quick hello” that will last a few minutes, as the U.S. and North Korea try to restart denuclearization and peace talks on the Korean peninsula, after months of stalemate following a failed summit in Hanoi, Vietnam.

It’s unclear if the meeting will actually happen — the invitation seemed impulsive, though North Korea reportedly called it a “very interesting suggestion.”

Mr. Trump talked up the theatrical backdrop known as the DMZ, a heavily armed relic of the Cold War structure and Korean War, which ended with an armistice in 1953 instead of everlasting peace.

“Nobody goes through that border. Just about nobody. That’s called a real border,” Mr. Trump said.

Mr. Trump invited Mr. Kim through his favorite medium, Twitter, ahead of his final meetings at the G-20 and a quick plane trip to this sprawling metropolis, where he’ll strategize with South Korean partners.

“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(?)!” Mr. Trump tweeted.

The president said Mr. Kim must follow him on social media, “because we got a call pretty quickly.”

At the same time, Mr. Trump characterized his tweet as a “feeler” and admitted he did not know of Mr. Kim’s whereabouts.

Mr. Trump did not elaborate on what he hoped to achieve with the handshake, after two previous summits with Mr. Kim failed to result in a firm deal.

“I just thought of it this morning,” Mr. Trump said during a meeting with Saudi Crown Prince Mohammad bin Salman at the G-20.

Mr. Trump tried to visit the DMZ in 2017, though his attempt was thwarted by heavy fog.

Previous presidents, including Barack Obama, have visited the heavily armed border, though Mr. Trump’s visit, if it happens, would take on a different flavor.

Rather than reinforcing the U.S. alliance with South Korea alone, it would signal an olive branch to Mr. Kim. The two leaders recently exchanged warm letters, signaling a thaw.

The hard part will be finding the right balance between reeling in North Korea’s nuclear and weapons programs, while offering the sanctions relief that Mr. Kim demands.

Mr. Trump said he ended the Hanoi summit in February after the North Koreans demanded sweeping sanctions relief in exchange for only a limited commitment to destroy part of their nuclear arsenal at the Yongbyon nuclear complex.

The president has taken credit for the status quo, which includes a self-imposed moratorium on nuclear testing and ballistic missile launches by Mr. Kim, plus the delivery of American remains from the secretive nation’s territory.

He said his embrace of the North Korean leader has been a “good thing,” despite the skeptics.

“If I didn’t become president … you’d be having a war right now with North Korea,” he said.

Mr. Moon will encourage Mr. Trump to be more flexible and pursue a step-by-step approach that generates momentum for denuclearization and reconciliation with the north.

The South Korean president has tied his legacy to the Korean peace process, so he wants to show progress.

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