President Donald Trump sent North Korean leader Kim Jong Un a letter, a government-controlled new agency reported Sunday (local time).

Mr Kim "said with satisfaction that the letter is of excellent content", the Korean Central News Agency reported.

"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.

President Donald Trump sent North Korean leader Kim Jong Un a letter, a government-controlled new agency reported Sunday (local time). (AP)

Nuclear talks between the US and North Korea broke down after the failed summit between Mr Kim and Mr Trump in February in Vietnam.

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.

Mr Trump and Mr Kim exchanged letters in 2018 after a summit in Singapore to discuss the nuclear issue.

White House spokeswoman Sarah Huckabee Sanders said at the time that the letters addressed their commitment to work toward North Korea's "complete denuclearisation".

Mr Trump and Mr Kim exchanged letters in 2018 after a summit in Singapore to discuss the nuclear issue. (AP)