The White House press secretary, Sarah Sanders, said Trump sent a letter and "correspondence between the two leaders has been ongoing."

Formal talks between the US and North Korea broke down after a failed summit between Kim and Trump in February in Vietnam. But earlier in June Trump told US reporters he received a "beautiful" letter from Kim, without revealing what was written. In an interview with TIME magazine last week, Trump said he also received a "birthday letter" from Kim that was delivered by hand a day before.

The official stances remain the same. The US is demanding that North Korea abandon its nuclear weapons entirely before international sanctions are lifted. North Korea is seeking a step-by-step approach in which moves toward denuclearisation are matched by concessions from the US, notably a relaxation of the sanctions.

Pyongyang's Korean Central News Agency's report on the Trump letter said Kim "said with satisfaction that the letter is of excellent content."

"Appreciating the political judging faculty and extraordinary courage of President Trump, Kim Jong Un said that he would seriously contemplate the interesting content," the agency said, without elaborating.

South Korea's presidential office said it sees the exchange of letters between Kim and Trump as a positive development for keeping the momentum for dialogue alive.

News of Trump's letter came days after Kim's summit with visiting Chinese President Xi Jinping, which experts say underscored China's importance in the diplomatic push to resolve the nuclear standoff with the North.

North Korean state media said Kim and Xi discussed the political situation surrounding the Korean Peninsula and reached unspecified consensus on important issues.

Xi is expected to meet with Trump next week in Japan during the G20 summit. Analysts say he could pass him a message from Kim about the nuclear negotiations.

Following a provocative run in weapons tests, Kim initiated negotiations with Seoul and Washington in 2018, which led to three summits with South Korea's president and his first with Trump in Singapore on June 12, 2018. Kim and Trump issued a vague statement at that summit saying they would work toward a nuclear-free Korean Peninsula without describing how.

The lack of substance and fruitless working-level talks set up the breakdown of Kim's second meeting with Trump, which the Americans blamed on excessive North Korean demands for sanctions relief in exchange for only a partial surrender of its nuclear capabilities.

Nuclear negotiations have been at a standstill since.

Trump and Kim also exchanged letters in 2018 after their first summit. Sanders said at the time that the letters addressed their commitment to work toward North Korea's "complete denuclearisation."

Australian Associated Press