President Trump said Friday he has received a “beautiful” letter from North Korean leader Kim Jong-un in the midst of renewed tensions.

“It was a very positive letter,” Mr. Trump said of the three-page, handwritten note. “I think we’ll have another meeting. He really wrote a beautiful letter. Maybe I’ll release the results of the letter, but it was very positive.”

Mr. Trump told reporters at the White House that the believes he and Mr. Kim will have another meeting. The letter hand-delivered Thursday comes after North Korea has launched a series of short-range missile tests.

Mr. Kim has conducted the tests in an apparent response to renewed joint military exercises by the U.S. and South Korea.

The president and Mr. Kim have held two summits aimed at denuclearizing North Korea, and they held an impromptu meeting this summer at the demilitarized zone between the North and South.

Mr. Trump did reveal that Mr. Kim conveyed his unhappiness about the joint military exercises in South Korea.

“He wasn’t happy with the war games, it’s a very small testing that we did,” Mr. Trump said. “He put that in the letter. I don’t like it, either.”

But the president said he agreed to the exercises because they involve South Korean forces taking over certain responsibilities from the U.S. military in the region.

“In the meantime, I say it again, there have been no nuclear tests,” he said of the North. “The missile tests have all been short-range, no ballistic missile tests, no long-range missiles.”

Defense Secretary Mark Esper on Friday called on South Korea to take part in the U.S.-led effort to protect vessels traveling through the Strait of Hormuz amid soaring tensions with Iran.

Mr. Esper made the request in a meeting between the newly confirmed Pentagon chief and the South Korean defense minister in Seoul, South Korean news agency Yonhap reported.

In a tweet following the meeting — part of the secretary’s first overseas trip since being confirmed to the top post — Mr. Esper said he is “confident the [U.S.-South Korean] alliance is ironclad.”

• Lauren Meier contributed this story.

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