United States President Donald Trump said he received "a beautiful letter" from North Korean leader Kim Jong-un this week, stressing "very good" relations between the two sides. 

In his speech in Missouri at a campaign rally on Friday (US time), Trump said, "Chairman Kim Jong-un sent me a beautiful letter two days ago," though he did not elaborate on details.

The remarks came less than two weeks after the White House said Trump received a written message from Kim, in which the North Korean leader requested a second meeting between the two.

Both Washington and Pyongyang have since floated the possibility of holding a second summit to move forward negotiations to dismantle North Korea's nuclear weapons program. Their historic first meeting was held in Singapore in June.

Pointing to the release of Americans who had been detained in the North and the return of remains of American soldiers who went missing during the 1950-53 Korean War, Trump said in his speech that the relationship between the US and North Korea is "going very well," adding that, "Let's see what happens."

He, however, said he is "in no rush," citing sanctions against Pyongyang still remain intact.

On Sunday, South Korean President Moon Jae-in plans to fly to the US to for a meeting with Trump, after holding a third summit with Kim in Pyongyang this week. (Yonhap)