US President Donald Trump has said he would like to meet North Korean leader Kim Jong-un this weekend at the demilitarised zone (DMZ) on the border of North and South Korea.

Mr Trump, who is in Osaka, Japan, for a G20 summit, is due to arrive in South Korea later today. He is scheduled to leave tomorrow and return to Washington.

"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(?)!" Mr Trump said on Twitter.

Mr Trump told reporters: "We'll be there and I just put out a feeler because I don't know where he is right now. He may not be in North Korea."

"If he's there, we'll see each other for two minutes, that's all we can, but that will be fine," he added. Mr Trump said he and Mr Kim "get along very well."

North Korea's mission to the United Nations did not immediately respond to a request for comment on Mr Trump’s offer.

US special envoy Stephen Biegun said yesterday the United States was ready to hold constructive talks with North Korea to follow through on a denuclearisation agreement reached by the two countries last year, South Korea's foreign ministry said.

Mr Biegun told his South Korean counterpart, Lee Do-hoon, that Washington wanted to make "simultaneous, parallel" progress on the agreement reached at a summit between Mr Trump and Mr Kim in Singapore last year, the ministry said in a statement.

Both sides had agreed to establish new relations and work towards denuclearisation of the Korean peninsula.

But negotiations have stalled since a second summit in Vietnam in February collapsed as the two sides failed to narrow differences between US calls for denuclearisation and North Korean demands for sanctions relief.

South Korea's presidential office said nothing was confirmed with regards to a Trump-Kim meeting.

"Nothing is fixed at the moment, and our previous position of hoping for dialogue between North Korea and the United States remains unchanged," the office said.

Hikers walk along a fence in the Demilitarised zone (DMZ) dividing the two Koreas

Mr Trump told reporters his offer for a meeting was a spur-of-the-moment idea. "I just thought of it this morning," he said.

Mr Trump wanted to visit the DMZ on a 2017 visit to South Korea but he was forced to put off the plan because of bad weather.

He said before departing for the G20 Osaka Summit that he did not expect to meet Mr Kim during his trip.

US Secretary of State Mike Pompeo said this week that a recent exchange of letters between the two boosted hopes for a restart of talks, calling it a "very real possibility."

Mr Trump told reporters the North Korean leader had sent him a birthday card, and so he sent him a letter in return.

North Korea's official KCNA news agency said Mr Trump's letter had "excellent content" and Mr Kim would "seriously contemplate" it, without elaborating.

Mr Trump has previously said publicly he had received a very warm "beautiful letter" from Mr Kim.

He has not divulged its contents, but the White House official, who did not want to be identified, described the letter as "very flowery."