WASHINGTON (Yonhap) -- US President Donald Trump has offered to meet with North Korean leader Kim Jong-un at the inter-Korean border during his two-day trip to South Korea.

Trump made the offer on Twitter on Saturday (Japan time), hours before he flew into Seoul after attending the Group of 20 summit in Osaka, Japan.

"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(?)!"   

There had been speculation that a Trump-Kim meeting could happen inside the Demilitarized Zone while the US president is in South Korea on Saturday and Sunday.

But Trump denied before leaving Washington on Wednesday that he planned to meet Kim, saying only that he may speak to the North Korean leader "in a different form."

 At a meeting in Osaka with Saudi Arabia's crown prince, Trump confirmed that he will be going to the DMZ. That part of the trip had previously been reported to be under consideration.

"We're going there," he said, according to news reports. "If he's there, we'll see each other for two minutes," he added, noting that he's unsure whether Kim is in the country.

If the two meet, it will be their third time seeing each other after their historic first summit in Singapore last June and their second summit in Vietnam in February.

When asked, Trump said he would have "no problem" stepping over the inter-Korean border to North Korea.

"Sure I would, I would. I'd feel very comfortable doing that. I'd have no problem," Trump told the press conference in Osaka, according to foreign news reports.

If he does cross the inter-Korean border, he will be the first US president ever to step on North Korean soil.

Trump said even if Kim shows up at the inter-Korean border, it would not be a formal meeting.

"We won't call it a summit. We'll call it a handshake," he told reporters.

North Korea was quick to respond to Trump's apparent proposal for a DMZ meeting, calling it a "very interesting suggestion."

Choe Son-hui, North Korea's first vice foreign minister, however, said her country has not received an official proposal in that regard.

"I am of the view that if the DPRK-U.S. summit meetings take place on the division line, as is 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," she said in a statement carried by the North's official Korean Central News Agency. DPRK stands for the North's official name, the Democratic People's Republic of Korea.

The US and North Korea have been negotiating the dismantlement of Pyongyang's nuclear weapons program in exchange for sanctions relief, but talks have stalled since the second summit ended without a deal.

An exchange of personal letters between Trump and Kim this month led to hopes for a revival of talks. The US president called Kim's letter "beautiful" and "very warm," while the North Korean leader praised Trump's note as "excellent."

Stephen Biegun, the US point man on the North, on Friday expressed the US.' willingness to hold "constructive" dialogue with the North. He also said the US was ready to advance the commitments made at the Singapore summit "in a simultaneous and parallel manner." The comments were made to his South Korean counterpart, Lee Do-hoon, in Seoul, according to South Korea's Foreign Ministry.

The Singapore summit yielded an agreement to establish "new" relations between the two countries and build a lasting peace regime on the Korean Peninsula. It also committed the North to work toward complete denuclearization in exchange for US security guarantees.

Trump said Saturday that he and Kim "seem to get along very well."

"It's good to get along because frankly if I didn't become president, you'd be right now in a war with North Korea," he claimed. "You'd be having a war right now with North Korea. And by the way that's a certainty. That's not like maybe."

On the tweet, he said: "All I did is put out a feeler if he'd like to meet. ... I just thought of it this morning."

Harry Kazianis, senior director of Korean studies at the Center for the National Interest in Washington, suggested that the White House's previous attempts to set up another meeting through official channels probably failed. 

"Now that he has been publicly called out -- with letters and a personal connection serving as the basis of a fragile detente -- I would bet Kim will travel to the DMZ to meet Trump," Kazianis said.

"While no major agreements will be signed, both sides can reaffirm their commitment to dialogue and diplomacy, essentially resetting the table for a future deal in the weeks and months to come."

South Korean President Moon Jae-in and Trump are expected to discuss ways to resume the negotiations. Moon has been eager to act as a mediator between North Korea and the US, and held three summits of his own with Kim last year.

The South Korean president said in a written interview with Yonhap News Agency and six other global news agencies this week that the US and the North have been engaged in back-channel talks over a third summit.

The North later denied that such discussions were taking place.

It marks Trump's second visit to South Korea since taking office. The first was in November 2017. Trump tried to go to the DMZ during that trip too, but heavy fog forced his helicopter to turn back.

Trump said Saturday that he will make a speech this weekend to US troops stationed in South Korea. (Yonhap)