U.S. President Donald Trump received a letter from North Korean leader Kim Jong Un as the two continue to discuss Pyongyang's commitment at a recent Singapore summit to rid itself of nuclear weapons, but no second meeting is currently planned, the White House said on Thursday.

White House spokeswoman Sarah Sanders said Trump had received a letter from Kim on Wednesday and had responded with a note that should be delivered shortly. Trump also posted a note on Twitter on Thursday thanking Kim for returning the remains of U.S. soldiers and saying he looked forward to seeing Kim again.

"He did receive a letter," Sanders told a White House briefing. "There is not a second meeting that is currently locked in or finalized. (We're) certainly open to that discussion, but there isn't a meeting planned."

"We have responded to Chairman Kim's letter - the president has - and that letter will be delivered shortly," Sanders told reporters.

She declined to elaborate on the details of the exchange, saying only that the notes "addressed their commitment from their joint statement ... that was made at the Singapore summit."

"They're going to continue working together towards complete and total denuclearization," Sanders added.

Trump and Kim met in Singapore in June, where they announced an agreement in which Kim reaffirmed his "unwavering" commitment to denuclearize. Little progress on that front has been made in the weeks since.

Trump's Twitter post on Thursday thanked Kim for returning the remains of some American war dead from the 1950-1953 Korean War.

Trump said in that tweet to Kim: "I look forward to seeing you soon!"

Trump has said repeatedly the deal he reached with Kim has been positive since North Korea has maintained a freeze on nuclear and missile tests and has begun returning U.S. war dead remains.

"I think it’s going to work out very well," he told supporters at a rally in Tampa, Florida, on Tuesday night. "No tests, no rockets flying. But we’ll see what happens."