President Trump, always one to think about the ratings, built anticipation ahead of a Sunday visit to the Demilitarized Zone that separates North and South Korea – abruptly offering to meet dictator Kim Jong Un for a handshake and even saying he’s willing to cross the border.

No sitting U.S. president has set foot in North Korea.

TRUMP OFFERS TO MEET KIM JONG UN AT NK BORDER

The tantalizing possibility of such a historic photo op – which Trump would cast as part of his effort to secure a nuclear deal, but Kim could exploit to burnish his cult of personality – was first dangled in a tweet.

“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 tweeted Friday. “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 is in Seoul after meeting with world leaders at the G20 summit in Japan.

While in Japan, Trump said at a news conference that he was “literally visiting the DMZ,” but wasn’t sure whether Kim would meet him.

Trump said 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.

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.

North Korea responded by calling the offer a “very interesting suggestion.”

There have been no public meetings between Washington and Pyongyang since the breakdown of a Trump-Kim summit in Vietnam earlier this year. The chances for a resumption of U.S.-North Korea diplomacy have brightened since Trump and Kim recently exchanged personal letters. Trump called Kim's letter "beautiful," while Kim described Trump's as "excellent," though the contents of their letters have not been disclosed.

TRUMP MEETS TOP K-POP BAND

The prospect now of a cross-border handshake and even a foray by an American president into the internationally isolated, hermetic North could, if nothing else, kick-start movement toward resuming formal negotiations – even as it surely would attract Democratic criticism that Trump is cozying up to dictators.

But Trump, at least publicly, discussed the offer to Kim in casual terms, leaving unclear the likelihood of such an encounter.

“All I did is put out a feeler, if you’d like to meet,” Trump said later of the message to Kim.

Despite the deadlocked nuclear negotiations, both Trump and Kim have described their personal relationship as good.

But in yet another reminder of North Korea's continued mistrust of the United States, its foreign ministry said Wednesday it won't surrender to U.S.-led sanctions and accused Washington of trying to "bring us to our knees."

Fox News’ Alex Pappas and The Associated Press contributed to this report.