North Korea on Sunday said Kim Jong Un supervised the launch of a new missile system — after President Trump said he got a letter from the leader apologizing for recent rocket tests and offering to resume nuclear talks.

The reclusive regime test-fired two short-range missiles on Saturday that flew about 250 miles before crashing into the sea between North Korea and Japan — the fifth launch in the past two weeks.

Kim, according to state-run media on Sunday, “expressed great satisfaction” after overseeing the launch.

The Hermit Kingdom’s official newspaper, the Rodong Sinmun, published photos of Kim watching with other military officials from what appeared to be an observation post.

The rocket launches by North Korea are seen as a protest against joint military exercises by the US and South Korea that Kim’s regime considers a rehearsal to an invasion.

Trump told reporters that he had received a “beautiful letter” from Kim.

“It was a very positive letter,” Trump said. “I think we’ll have another meeting. He really wrote a beautiful, three-page — I mean, right from top to bottom — a really beautiful letter.”

North Korea launched the missiles shortly afterward.

The president posted on Twitter Saturday morning that Kim wanted to begin negotiations once the military games conclude and included a “small apology for testing the short range missiles, and that this testing would stop when the exercises end.”

Talks between Pyongyang and Washington have stalled since Trump’s summit with Kim in June on the border between the Koreas.

With Post wires