U.S. President Donald Trump said Wednesday that "tremendous progress" was being made with North Korea following a third summit between the leaders of the two Koreas.

Trump told reporters at the White House that there was very good news from North and South Korea, adding he received a tremendous letter from North Korean leader Kim Jong-un three days ago. 

He said that before he came into office, a war with North Korea seemed inevitable, but the U.S. is now making a lot of progress with Pyongyang, citing North Korea releasing American prisoners, returning remains of U.S. soldiers from the Korean War and stopping its nuclear and missile tests.

Trump said that at least on a personal basis, his relationship with Kim is very good and has very much calmed down, adding the U.S. would wait and see what North Korea does next. 

When asked if he will be meeting Kim soon, he responded that they will. 

South Korean President Moon Jae-in and North Korean leader Kim Jong-un held meetings in Pyongyang on Tuesday and Wednesday and jointly reaffirmed their commitment to make the peninsula free of nuclear weapons.

Kim committed to take additional steps to dismantle the North's ballistic missile programs and expressed his willingness to shut down its key nuclear facility if the U. S. takes reciprocal steps.