OSAKA, Japan — President Donald Trump made an extraordinary public offer Saturday to meet North Korean leader Kim Jong Un, inviting him to shake hands “and say hello” in the demilitarized zone between North and South Korea.

Although it was unclear whether the two would indeed meet on Sunday, when Trump said he plans to visit the DMZ, both sides suggested even the invitation was a step in the right direction amid stalled nuclear talks.

North Korea called the idea "very interesting" while Trump said that the North Koreans had reached out immediately and that Kim was "very receptive."

"I can tell you exactly what they did: respond very favorably," Trump said in Osaka as he wrapped up his trip to Japan for the G-20 summit.

Trump had issued the invitation to the North Korean leader on Twitter as he started his final day in Japan before flying to Seoul, where Trump planned to meet with the South Korean president.

“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 (?)!” the president tweeted.

Meeting minutes later with Saudi Crown Prince Mohammed bin Salman, Trump said he'd merely "put out a feeler if he'd like to meet." He said the invite followed a "very beautiful birthday card" that Kim had sent him and a return letter that Trump had sent to Kim in Pyongyang.

"If he's there, we'll see each other for two minutes. That's all we can," Trump said.

North Korea's government responded hours later, calling it a "very interesting suggestion" but not indicating whether Kim would meet with Trump.

"We have not received an official proposal," Choe Son Hui, a senior North Korean diplomat, was quoted as saying by state-run news agency KCNA.

Although Trump's trip to South Korea had prompted speculation he would likely visit the DMZ, no such visit had been formally announced, in line with typical security protocols. But Trump on Saturday made it clear he did intend to visit, telling reporters, "We're going there. We're going to look at it."

Trump said that he and the North Korean leader "seem to get along very well," calling it "a good thing." He said it was a "certainty" that if he hadn't been elected to the White House, the United States would be in a war with the country.

If the meeting takes place, it will be the first time a U.S. and North Korean leader have met in the DMZ, which despite its name is the most heavily fortified border in the world. It would also mark the third face-to-face meeting between Kim Jong Un and Trump, who made history in 2018 as the first U.S. president to meet with a North Korean leader while in office.

"We won't call it a summit, we'll call it a handshake," Trump said.

Yet asked whether it would mark a failure or a rejection if Kim did not take him up on the offer, Trump replied flatly, "No."

The president said he'd taken into consideration the possibility it would be perceived that way before issuing the invitation, but that it didn't bother him if Kim couldn't make it.

Trump’s last summit with the North Korean leader — in Hanoi, Vietnam, in February — collapsed abruptly, with a planned signing ceremony scrapped and Trump explaining to reporters that “sometimes you have to walk.”

At the center of that failure, U.S. officials have said, was Kim’s insistence that all nuclear sanctions be lifted in exchange for only some concessions sought by the U.S. from Pyongyang related to its nuclear program.

In the run-up to Trump’s trip to Japan for the Group of 20 summit and his subsequent stop in Seoul, there were signs that a potential tête-à-tête with Kim could be in the works. South Korea's president said publicly that U.S. and North Korean officials were holding “behind-the-scenes talks” to arrange a third summit between their leaders, although North Korea’s foreign ministry later seemed to distance itself from that notion by saying that South Korea should cease trying to mediate with Washington.

It’s unclear how much if any progress has been made between the U.S. and North Korea since the Hanoi summit in bridging the serious divides that led to its collapse. Still, the White House has acknowledged that Trump and Kim have continued to exchange correspondence since — messages that Trump has described as “beautiful letters” from the authoritarian leader of the nuclear-armed nation.

U.S. presidents and vice presidents occasionally visit the DMZ, a no-man’s land that includes a designated area where North and South Korean officials periodically have met. High-level U.S. visits are typically shrouded in secrecy and accompanied by significant security arrangements, with American leaders often holding photo-ops from a vista where they can peer through binoculars at North Korean soldiers not far away.

As reporters were briefly allowed in at the start of Trump's meeting with Crown Prince Mohammed, Trump paused momentarily when a reporter asked about the death of former Washington Post columnist Jamal Khashoggi, who was killed by Saudi agents last year in the Saudi Consulate in Istanbul. Then Trump moved on without answering, ushering reporters out of the room by saying, "Thank you very much."