SEOUL, South Korea — For six decades, joint exercises held by the militaries of South Korea and the United States have been the most visible and celebrated display of the alliance. Each year, their Marines storm South Korean beaches together, their tanks spew orange-red flames and their warplanes run mock bombing raids on imaginary North Korean nuclear targets.

Such scenes, broadcast on prime-time television, have been a frequent reminder for South Koreans of how much the country depends on the alliance for its security.

Now they are dealing with a jarring new reality: an American president who does not like the drills, at least in part because they cost too much. President Trump, who in June suspended the exercises after meeting with the North’s leader, Kim Jong-un, reaffirmed his misgivings on Wednesday, saying he saw “no reason at this time to be spending large amounts of money on joint U.S.-South Korea war games.”

His remarks on Twitter came a day after his defense secretary, Jim Mattis, seemed to open the door to resuming the drills. Mr. Trump said that he could do so “instantly” if he chose, and that, if he did, the joint exercises would be “far bigger than ever before.”