Donald Trump may become the first U.S. president to set foot in North Korea when he visits the demilitarized zone separating the two Koreas on Sunday.

Trump has invited North Korean leader Kim Jong Un for a quick meeting at the DMZ's Panmunjom border village. Before landing in Seoul, Trump said he would feel "very comfortable" stepping across the border into North Korea.

"Virtually a handshake," Trump said of the possible meeting. "But that's OK. A handshake means a lot."

Though it isn't clear the meeting will go beyond a photo opportunity, many hope a DMZ handshake could restart stalled nuclear talks.

Speaking alongside Trump on Sunday, South Korean President Moon Jae-in said "he could truly feel the flower of peace was blossoming on the Korean peninsula" when he saw Trump's invitation to Kim.

"I believe that picture in itself would represent a historic event and also would be a significant milestone in terms of the peace process," Moon said of a DMZ meeting.

Kim has not publicly responded to the invitation, which Trump sent via Twitter. North Korea's vice foreign minister on Saturday called Trump's offer an "interesting suggestion."

It would be the third summit between Kim and Trump, following meetings in Singapore last June and in Vietnam in February. Whereas those meetings were held at hotels, Panmunjom would provide a much more dramatic setting.

With its iconic light-blue buildings that straddle the North-South border, Panmunjom is the only place along the 250-kilometer-long DMZ where North and South Korean soldiers can stand face-to-face.

Working-level talks stall

Since the meeting in Hanoi, North Korea has not responded to U.S. requests to resume working-level talks. North Korea is unhappy with the U.S. refusal to relax sanctions in exchange for limited steps to dismantle its nuclear program.

Given that neither side has publicly softened their negotiating position, progress may be unlikely for now.

"It's hard to see much more coming out of this other than showing the world that Trump and Kim are still on speaking terms after Hanoi," said Vipin Narang, a nuclear expert and professor at the Massachusetts Institute of Technology.

Though international attention may focus on a possible Trump-Kim meeting at the DMZ, a key indicator of progress will be whether North Korea agrees to meet with Steve Biegun, the U.S. special representative for North Korea.

U.S. officials, including Biegun, have given mixed signals about whether they are open to an incremental approach, whereby Pyongyang would give up its nuclear program in stages in exchange for reciprocal steps by Washington.

Trump wants Kim to agree to a "big deal," under which Kim agrees to completely abandon his nuclear program.

The U.S. refusal to relax sanctions on North Korea has prevented South Korean President Moon from implementing inter-Korean projects.

"If Trump really wanted to send a signal to Kim that progress is still possible, he would cooperate with Seoul and allow for some of the inter-Korean economic cooperation to move forward," says Jenny Town, a Korea specialist at the Stimson Center.

Moon on Sunday confirmed he would accompany Trump at the DMZ.

Will Kim show?

Some speculate that Kim may not show up at the DMZ to meet Trump.

"I think Kim has much more to gain with a no-show than showing up for another photo op, with nothing substantive gained," says Sung-Yoon Lee, a Korea expert at Tufts University's Fletcher School.

Instead, Lee speculates Kim may choose to have his sister Kim Yo Jong deliver a letter to Trump.

"Kim can dictate the terms and pace of engagement better with a no-show," he says.

But Narang, the MIT professor, disagrees, saying Kim could exploit such a meeting to further bolster his reputation with his domestic audience.

"For Kim, the fact that Trump reached out -- in some ways desperately on Twitter -- may help him considerably at home," Narang says.

Historic moment

If Kim does show up, Trump's visit to the DMZ could well make history.

Though U.S. presidents frequently visit the DMZ during stops in South Korea, none has ever stepped across the border into North Korea. Though such a move would be historic, it's not clear what it would mean practically, some analysts warn.

"President Trump delights in doing things no president has done before," says Bonnie Glaser with the Center for Strategic and International Studies. But for Trump, "a step inside North Korea might not signify any policy intentions whatsoever."