U.S. President Donald Trump on Saturday expressed his willingness to "shake hands" with North Korean leader Kim Jong Un at the Demilitarized Zone on the border of the two Koreas, eliciting a positive response from Pyongyang.

"We may be meeting Chairman Kim," Trump said at a press conference before heading to South Korea after the Group of 20 summit in Osaka. "Kim Jong Un was very receptive and he responded, so we'll see."

If his third face-to-face contact with Kim is realized, it would be a casual meeting rather than a formal summit, Trump suggested, but he added he is still not sure whether the meeting will take place.

Trump also said he would feel "very comfortable" stepping into North Korea by crossing the DMZ if he meets with Kim.

Earlier in the day Trump said in a Twitter post, "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(?)!"

North Korea quickly responded to Trump's offer, with the state-run Korean Central News Agency quoting a diplomat as saying that although no official proposal has been received, the U.S. president made a "very interesting suggestion."

Trump, who is slated to hold talks with President Moon Jae In in Seoul on Sunday and likely visit the DMZ, said Pyongyang reacted "very favorably."

Trump's DMZ visit would most likely take place at the inter-Korean truce village of Panmunjeom, where Moon and Kim met for talks twice last year.

At the outset of talks with Saudi Arabia's Crown Prince Mohammad bin Salman on Saturday morning in Osaka, Trump, confirming that he plans to visit the DMZ, said that if Kim comes, "We'll see each other for two minutes. That's all we can. But that will be fine."

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

Later in the day, Vice Foreign Minister Choe Son Hui said that if Trump and Kim really meet at the DMZ, "it would serve as another meaningful occasion in further deepening the personal relations between the two leaders and advancing the bilateral relations."

But North Korea has "not received an official proposal in this regard," said the diplomat in charge of Pyongyang's diplomacy with Washington in an English statement carried by KCNA.

South Korea's presidential office, meanwhile, said Saturday no arrangements have been made for a meeting between Trump and Kim.

Trump's remarks came as U.S.-North Korea negotiations remain stalled following the collapse of their second summit in Hanoi in late February. Despite the rupture, Trump has voiced eagerness to continue talks with Kim.

Earlier this month, the U.S. and North Korean leaders exchanged letters, in a sign that their relations are still good.

North Korea's official news agency reported last Sunday that Kim received a personal letter from Trump and expressed "satisfaction" with it, although KCNA did not elaborate on what was communicated.

On June 11, the eve of the one-year anniversary of the first U.S.-North Korea summit in Singapore, Trump told reporters that he had received a "beautiful" letter from Kim.

At their first meeting, Kim and Trump agreed that the United States would provide security guarantees to North Korea in return for "complete denuclearization" of the Korean Peninsula.

The two leaders, however, fell short of a deal at their second summit in the Vietnamese capital due largely to the gap between Washington's insistence on denuclearization and Pyongyang's demand for sanctions relief.

Arguing that Pyongyang has already implemented concrete steps to attain denuclearization of the peninsula, Kim has called on Washington to fulfill the Singapore agreement and ease sanctions. But Trump is believed to be reluctant to compromise.

North Korea has recently resumed provocative actions such as firing what were thought to be short-range ballistic missiles in early May.

In a speech to the country's legislature in April, Kim asked the United States to shift its policy on denuclearization negotiations by the end of this year, criticizing it for making what he claimed are one-sided demands.

Kim met with Chinese President Xi Jinping in Pyongyang last week and he is believed to have attempted to obtain Beijing's help to move negotiations forward with Washington.

Xi held bilateral talks with Trump on Saturday on the sidelines of the G-20 summit. At the meeting, Xi urged Trump to resume negotiations with North Korea as soon as possible, China's state-run Xinhua News Agency reported.

China and North Korea fought together in the 1950-1953 Korean War against U.S.-led United Nations forces, and Beijing remains Pyongyang's closest ally. The United States and North Korea have no diplomatic ties.