South Korean President Moon Jae-in, right, and U.S. President Donald Trump arrive for an expanded meeting at the presidential Blue House in Seoul, Sunday, June 30, 2019. (Kim Hong-Ji/Pool Photo via AP)

SEOUL, South Korea (AP) — President Donald Trump will meet Sunday with North Korea's Kim Jong Un at the Demilitarized Zone separating the North and South, a day after he issued an unprecedented invitation and expressed willingness to cross the border for what would be a history-making photo op.

South Korean President Moon Jae-in announced that Kim accepted Trump's invitation to meet when the U.S. president visits the heavily fortified site at the Korean border village of Panmunjom.

Moon praised the two leaders for "being so brave" to hold the meeting and said, "I hope President Trump will go down in history as the president who achieves peace on Korean Peninsula."

Trump said he looked forward to meeting with Kim, but sought to tamp down expectations, predicting it would be "very short," he said. "Virtually a handshake, but that's OK. A handshake means a lot."

Officials spent Sunday morning working out logistical and security details, Trump said during an earlier appearance with Moon.

The invitation, while long rumored in diplomatic circles, still came across as an impulsive display of showmanship by a president bent on obtaining a legacy-defining nuclear deal. North Korea responded by calling the offer a "very interesting suggestion."

Presidential visits to the DMZ are traditionally carefully guarded secrets for security reasons. White House officials couldn't immediately say whether Kim had agreed to meet with Trump. The president himself claimed before flying from Japan to South Korea that he wasn't even sure Kim was in North Korea to accept the invitation.

"All I did is put out a feeler, if you'd like to meet," Trump said in Japan. He added, somewhat implausibly: "I just thought of it this morning."

Before arriving in Seoul, Trump said at a news conference in Japan that he'd "feel very comfortable" crossing the border into North Korea if Kim showed up, saying he'd "have no problem" becoming the first U.S. president to step into North Korea.

His comments followed hours after Trump asked for Kim to meet him 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(?)!" he tweeted.

It was not immediately clear what the agenda, if any, would be for the potential third Trump-Kim meeting.

"If he's there we'll see each other for two minutes," Trump predicted.

Such a spectacle would present a valuable propaganda victory for Kim, who, with his family, has long been denied the recognition they sought on the international stage.

Despite Trump's comments Saturday, he had told The Hill newspaper in Washington in an interview this past week that he would be visiting the DMZ and "might" meet with Kim. The paper reported it had withheld Trump's comments, citing security concerns by the White House.

North Korea's first vice foreign minister, Choe Son Hui, said the meeting, if realized, would serve as "another meaningful occasion in further deepening the personal relations between the two leaders and advancing the bilateral relations."

Meeting with Trump at South Korea's presidential Blue House on Sunday, Moon said when he saw Trump's invitation to Kim, "I could really feel that the flower of peace was truly blossoming on the Korean peninsula." Moon, who will accompany Trump to the DMZ, added that the meeting - if it happens - would be a "significant milestone in the peace process."

Trump's summit with Kim in Vietnam earlier this year collapsed without an agreement for denuclearizing the Korean Peninsula. He became the first sitting U.S. president to meet with the leader of the isolated nation last year, when they signed an agreement in Singapore to bring the North toward denuclearization.

Substantive talks between the nations have largely broken down since then. The North has balked at Trump's insistence that it give up its weapons before it sees relief from crushing international sanctions.

Still, Trump has sought to praise Kim, who oversees an authoritarian government, in hopes of keeping the prospects of a deal alive, and the two have traded flowery letters in recent weeks.

Every president since Ronald Reagan has visited the 1953 armistice line, except for George H.W. Bush, who visited when he was vice president. The show of bravado and support for South Korea, one of America's closest military allies, has evolved over the years to include binoculars and bomber jackets.

Trump, ever the showman, appears to be looking to one-up his predecessors with a Kim meeting.

As he left the White House for Asia earlier this week, Trump was asked whether he'd meet with Kim.

"I'll be meeting with a lot of other people ... but I may be speaking to him in a different form," Trump said.

Such trips to the demilitarized zone are usually undertaken under heavy security and the utmost secrecy. Trump tried to visit the DMZ when he was in Seoul in November 2017, but his helicopter was grounded by heavy fog.

Trump has staked his self-professed deal-making reputation on his rapprochement with the North and has even turned it into a campaign rallying cry. Trump has repeatedly alleged that if he had lost the 2016 presidential campaign, the U.S. would be "at war" with North Korea over its nuclear weapons and ballistic missile programs.

The meeting would come at a time of escalating tensions. While North Korea has not recently tested a long-range missile that could reach the U.S., last month it fired off a series of short-range missiles. Trump has brushed off the significance of the tests, even as his own national security adviser, John Bolton, has said they violated U.N. Security Council resolutions.

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Associated Press writers Hyung-jin Kim and Kim Tong-hyung in Seoul, South Korea, and Darlene Superville and Jill Colvin in Washington contributed to this report.

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Follow Lemire on Twitter at http://twitter.com/@JonLemire and Miller at http://twitter.com/@zekejmiller

President Donald Trump speaks to Korean business leaders in Seoul, Sunday, June 30, 2019. (AP Photo/Susan Walsh)
FILE - In this June 14, 2019, file photo, hikers and journalists walk along the DMZ Peace Trail in the demilitarized zone in Goseong, South Korea. Eyeing a history-making photo opportunity, U.S. President Donald Trump on Saturday, June 29, 2019, issued a Twitter invitation to North Korea's Kim Jong Un to join him for a hand shake during a visit by Trump to the demilitarized zone with South Korea. (AP Photo/Ahn Young-joon, File)
U.S. President Donald Trump arrives at Osan Air Base in Pyeongtaek, South Korea, Saturday, June 29, 2019. (Kim Hong-Ji/Pool Photo via AP)
A banner shows images, from left, of North Korean leader Kim Jong Un, South Korean President Moon Jae-in and U.S. President Donald Trump, displayed by protesters who demand the peace on the Korean peninsula near U.S. Embassy in Seoul, South Korea, Saturday, June 29, 2019. Eyeing a history-making photo opportunity, Trump on Saturday issued a Twitter invitation to Kim to join him for a hand shake during a visit by Trump to the demilitarized zone with South Korea. (AP Photo/Ahn Young-joon)
U.S. President Donald Trump, left, and South Korean President Moon Jae-in, right, pose for a photo during a visit to the tea house on the grounds of the Blue House in Seoul, South Korea, Saturday, June 29, 2019. Trump is making a quick trip to Seoul after attending the G-20 summit in Osaka, Japan. (AP Photo/Susan Walsh)
South Koreans carry a huge U.S. flag during a rally to welcome U.S. President Donald Trump's visit in Seoul, South Korea, Saturday, June 29, 2019. North Korea said Saturday President Donald Trump's offer to meet leader Kim Jong Un at the Korean Demilitarized Zone is a
FILE - In this March 25, 2012, file photo, then U.S. President Barack Obama, second left, looks through binoculars to see North Korea from Observation Post Ouellette in the Demilitarized Zone, the tense military border between the two Koreas, in Panmunjom, South Korea. President Donald Trump is inviting North Korea's Kim Jong Un to shake hands during a visit to the demilitarized zone with South Korea. Trump is scheduled to visit South Korea later Saturday after meetings at the Group of 20 summit in Osaka, Japan. (AP Photo/Susan Walsh, File)
FILE - U.S. President George W. Bush, right, looks out at North Korea from Observation Point Ouellette in the Demilitarized Zone, the tense military border between the two Koreas, in Panmunjom, Korea, on Feb. 20, 2002. President Donald Trump is inviting North Korea's Kim Jong Un to shake hands during a visit to the demilitarized zone with South Korea. Trump is scheduled to visit South Korea later Saturday after meetings at the Group of 20 summit in Osaka, Japan. (AP Photo/J. Scott Applewhite, File)
FILE - In this Wednesday, Dec. 12, 2018, file photo provided by South Korea Defense Ministry, South Korean army Col. Yun Myung-shick, right, shakes hands with North Korean army Lt. Col. Ri Jong Su before crossing the Military Demarcation Line inside the Demilitarized Zone (DMZ) to inspect the dismantled North Korean guard post in the central section of the inter-Korean border in Cheorwon. President Donald Trump is inviting North Korea's Kim Jong Un to shake hands during a visit to the demilitarized zone with South Korea. Trump is scheduled to visit South Korea later Saturday after meetings at the Group of 20 summit in Osaka, Japan. (South Korea Defense Ministry via AP, File)
FILE - In this Nov. 15, 2018, file photo, smoke from an explosion rises as part of the dismantling of a South Korean guard post in the Demilitarized Zone dividing the two Koreas in Cheorwon, South Korea, as a North Korean guard post sits high in the upper left. President Donald Trump is inviting North Korea's Kim Jong Un to shake hands during a visit to the demilitarized zone with South Korea. Trump is scheduled to visit South Korea later Saturday after meetings at the Group of 20 summit in Osaka, Japan. (Jung Yeon-je/Pool Photo via AP, File)
FILE - In this July 11, 1993, file photo, U.S. President Bill Clinton takes the lens caps off a pair of binoculars at Camp Casey from the Ouellette guard post in the Demilitarized Zone (DMZ), the tense military border between the two Koreas, in Panmunjom, South Korea. President Donald Trump is inviting North Korea's Kim Jong Un to shake hands during a visit to the demilitarized zone with South Korea. Trump is scheduled to visit South Korea later Saturday after meetings at the Group of 20 summit in Osaka, Japan. (AP Photo/Greg Gibson, File)
FILE - In this April 27, 2018, file photo, North Korean leader Kim Jong Un, left, prepares to shake hands with South Korean President Moon Jae-in over the military demarcation line at the border village of Panmunjom in Demilitarized Zone. U.S. President Donald Trump is inviting North Korea's Kim Jong Un to shake hands during a visit to the demilitarized zone with South Korea. Trump is scheduled to visit South Korea later Saturday after meetings at the Group of 20 summit in Osaka, Japan. (Korea Summit Press Pool via AP, File)
FILE - In this Aug. 18, 1976, file photo, North Korean soldiers attack United Nations Command personnel wearing helmets at the truce village of Panmunjom, South Korea. President Donald Trump is inviting North Korea's Kim Jong Un to shake hands during a visit to the demilitarized zone with South Korea. Trump is scheduled to visit South Korea later Saturday after meetings at the Group of 20 summit in Osaka, Japan. (Yonhap via AP, File)
In this June 12, 2019, photo, North Korean soldiers look at the South side, seen during a press tour at the Panmunjom in the Demilitarized Zone (DMZ), South Korea. U.S. President Donald Trump on Saturday, June 29, 2019, invited North Korean leader Kim Jong Un to shake hands during a visit by Trump to the DMZ with South Korea. (AP Photo/Lee Jin-man)