North Korean leader Kim Jong Un and South Korean President Moon Jae-in have met for the second time in a month to discuss carrying out the peace commitments they reached in their first summit.

The pair also talked about Mr Kim’s potential meeting with President Donald Trump next month.

South Korean presidential spokesman Yoon Young-chan said Mr Moon will reveal the outcome of his surprise meeting with Mr Kim on Sunday.

The presidential Blue House did not immediately provide more details.

The meeting at a border truce village came hours after South Korea expressed relief over revived talks for a summit between President Trump and Mr Kim following a whirlwind 24 hours that saw the US leader cancel the highly anticipated meeting, before saying it is potentially back on.

President Trump later tweeted that the summit, if it does happen, will likely take place on June 12 in Singapore as originally planned.

In their first summit in April, Mr Kim and Mr Moon announced vague aspirations for a nuclear-free Korean Peninsula and permanent peace, which Seoul has tried to sell as a meaningful breakthrough to set up the summit with President Trump.

But relations between the rival Koreas have chilled in recent weeks, with North Korea cancelling a high-level meeting with Seoul over South Korea’s participation in regular military exercises with the United States and insisting that it will not return to talks unless its grievances are resolved.

South Korea, which brokered the talks between Washington and Pyongyang, was caught off guard by President Trump’s abrupt cancellation of the summit in which he cited hostility in recent North Korean comments.

Mr Moon said President Trump’s decision left him “perplexed” and was “very regrettable”.

He urged Washington and Pyongyang to resolve their differences through “more direct and closer dialogue between their leaders”.

President Trump’s back-and-forth over his summit plans with Mr Kim has exposed the fragility of Seoul as an intermediary.

It fanned fears in South Korea that the country may lose its voice between a rival intent on driving a wedge between Washington and Seoul and an American president who thinks less of the traditional alliance with Seoul than his predecessors.

President Trump’s decision to pull out of the summit with Mr Kim came just days after he hosted Mr Moon in a White House meeting where he openly cast doubts on the Singapore meeting but offered no support for continued inter-Korean progress, essentially ignoring the North’s recent attempts to coerce the South.

In his letter to Mr Kim, President Trump objected specifically to a statement from senior North Korean diplomat Choe Son Hui.

She referred to Vice President Mike Pence as a “political dummy” for his earlier comments on North Korea and said it was up to the Americans whether they would “meet us at a meeting room or encounter us at nuclear-to-nuclear showdown”.

North Korea issued an unusually restrained and diplomatic response to President Trump, saying it is still willing to sit for talks with the United States “at any time, [in] any format”.

“The first meeting would not solve all, but solving even one at a time in a phased way would make the relations get better rather than making them get worse,” North Korean Vice Foreign Minister Kim Kye Gwan said in a statement carried by Pyongyang’s official Korean Central News Agency, which mainly targets external audience.

Notably, the statement did not appear in Saturday’s edition of Rodong Sinmun, the official mouthpiece of the North’s ruling party that’s widely read by North Koreans.