US President Donald Trump received a letter from North Korean leader Kim Jong Un asking for a second meeting and the White House is already looking at scheduling one, White House spokeswoman Sarah Sanders said on Monday.

The two leaders have been discussing North Korea's nuclear program since their unprecedented June 12 summit which has been criticized for being short on concrete details about how and whether Kim is willing to give up on a nuclear weapons program that threatens the United States.

Trump told reporters on Friday that a personal letter from Kim was on the way. "It was a very warm, very positive letter," Sanders said at a briefing.

"The primary purpose of the letter was to request and look to schedule another meeting with the president which we are open to and are already in the process of coordinating that," Sanders said.

Sanders told reporters the letter exhibited "a continued commitment to focus on denuclearization of the peninsula." She said a military parade in Pyongyang on Sunday was "a sign of good faith" because it did not feature any long-range nuclear missiles.

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