Pentagon officials said Tuesday they’ll stay out of President Trump[1]’s landmark diplomacy with Kim Jong-un[2] — but they also emphasized that, so far, military leaders have gotten no formal instructions to follow through on the president’s words and immediately cancel joint military exercises with close ally South Korea.

Officials said Defense Secretary James N. Mattis has been kept in the loop as the White House opened public negotiations with the previously reclusive North Korean leader during a landmark summit in Singapore on Monday night. They said Mr. Mattis was not caught off guard and had been consulted before Mr. Trump[3] shockingly declared the U.S. would cease the joint military exercises, which the president called “provocative” and suggested would be a barrier to lasting peace with Pyongyang.

The exercises — two drills held in the spring, and another in the late summer or early fall — have become a staple of the American presence on the Korean peninsula and offer regular reassurances to South Korea, Japan, and other allies in the region that the U.S. is fully prepared to deter any possible North Korean aggression.

For now, U.S. military leaders say they’ve received no orders to cancel an upcoming drill scheduled for later this summer, a massive yearly exercise known as Ulchi Freedom Guardian. Last year, the 10-day computer-simulated exercise involved more than 17,000 U.S. troops, in addition to South Korean forces, according to the Defense Department.

Still, despite the uncertainty around whether the exercise is still scheduled, Pentagon spokesperson Dana White told Reuters on Tuesday “there were no surprises” when Mr. Trump[4] raised the issue following his meeting with Mr. Kim[5]. Beyond that, the Defense Department had little else to say, sticking to Mr. Mattis’ stated policy of keeping the military out of diplomatic efforts.

“The Department of Defense welcomes the positive news coming out of the summit and fully supports the ongoing, diplomatically-led efforts with the Democratic People’s Republic of Korea,” Ms. White said in a statement later Tuesday. “Our alliances remain ironclad, and ensure peace and stability in the region. The presidential summit outcome is the first step along the path to the goal: complete, verifiable and irreversible denuclearization of the Korean Peninsula and a free and open Indo-Pacific.”

While Mr. Mattis apparently was informed that the president intended to raise the issue, it’s unclear how far the news had traveled through the Pentagon before Mr. Trump[6] brought it up.

“It’s a very provocative situation,” the president said of the drills. “No. 1, we save money. No. 2, I think it’s something they very much appreciate [during the nuclear negotiations].”

He said the U.S. will not be removing any of its roughly 28,000 troops stationed in South Korea in the near term, though he did say that was one of his ultimate goals....

“No, we’re not reducing anything,” he

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