SEOUL, South Korea — For South Koreans who have long felt threatened by nuclear war, seeing President Trump and North Korea’s leader shake hands and sign an agreement on improving ties brought relief, if not closure, to the decades-old standoff.

But the optimism was quickly tempered by a shocker.

Hours after the summit meeting with Kim Jong-un in Singapore was over, Mr. Trump said he planned to end annual joint military exercises with South Korea, emphasizing their expense.

Mr. Trump suggested that he was ending the “very provocative” war games as an incentive for North Korea to denuclearize, granting the North one of its most avidly sought objectives even before the country has begun dismantling its nuclear weapons.

North Korea has long insisted that it would not relinquish its nuclear weapons program unless the United States removed its “hostile policies.” The North has cited military drills between the United States and South Korea as a prime example of American hostility, calling them rehearsals for invasion. Washington and Seoul have always dismissed such accusations as propaganda.