Officials declined to say whether Mr. Trump was seeking options for a full or partial reduction of troops, though a full withdrawal was unlikely. They emphasized that rethinking the size and configuration of the American force was overdue, regardless of the sudden flowering of diplomacy with North Korea.
But Mr. Trump’s meeting with Mr. Kim injects an unpredictable new element. His enthusiasm for the encounter — and the prospect of ending a nearly 70-year-old military conflict between the two Koreas — has raised concerns that he may offer troop cuts in return for concessions by Mr. Kim.
Defense Secretary Jim Mattis added to those concerns last Friday when he suggested that the future of the American military presence might be on the table.
“That’s part of the issues that we’ll be discussing in negotiations with our allies first, and of course with North Korea,” he said. “For right now, we just have to go along with process, have the negotiations and not try to make preconditions or presumptions about how it’s going to go.”
A spokesman for the Joint Chiefs of Staff, Col. Patrick Ryder, said he had no information about troop options being prepared for the president.
For Mr. Trump, withdrawing troops would have multiple benefits, said Victor D. Cha, a Korea scholar at Georgetown University who was for a time under consideration to be ambassador to Seoul. It would appeal to his political base, save the United States money and give him a valuable chit in his negotiation with Mr. Kim.
“But from the perspective of the U.S.-South Korea alliance,” Mr. Cha said, “it would represent a major retrenchment.”
Kelly E. Magsamen, a top Asia policy official at the Pentagon during the Obama administration, said, “U.S. presence in South Korea is a sacrosanct part of our alliance.”
The South Korean government reiterated this week that the troops were still needed and would not be pulled out as a result of a peace treaty with North Korea. But even close allies of President Moon Jae-in have raised doubts about the rationale for a long-term American presence.
“What will happen to U.S. forces in South Korea if a peace treaty is signed?” Moon Chung-in, an adviser to the president, said in a widely read article published this week. “It will be difficult to justify their continuing presence.”
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Mr. Kim recently declared, through South Korean officials, that he would drop the North’s longstanding insistence that American troops leave the peninsula. Some experts argue that watching American soldiers depart is far less important to him than winning relief from economic sanctions.
For years, the American presence has been more important as a symbol of deterrence than as a fighting force. At their current levels, the troop numbers are down by about a third from the level in the 1990s.
As the South Koreans have become a premier fighting force — with their own special operations forces, the ability to oppose the North’s artillery along the Demilitarized Zone and now their own cyberforces — they have become less dependent on the United States. Most American troops have pulled back to well south of Seoul.
Since President George Bush removed tactical nuclear weapons from South Korea in the early 1990s, the nuclear deterrent against the North has been based far away, in missile silos on the continental United States, submarines in the Pacific or bombers based on Guam.
Mr. Trump is not the first president to push for troop reductions. Jimmy Carter ran for office on a promise to withdraw all ground combat forces, in part to protest South Korea’s autocratic government at the time. Resistance from the military and Congress stymied his efforts. In 2004, George W. Bush’s defense secretary, Donald H. Rumsfeld, shifted nearly 10,000 troops from South Korea to the Iraq war.
During the Obama administration, former officials said, the Pentagon was always reluctant to consider troop reductions or the suspension of joint military exercises when the White House talked about potential pathways to ridding North Korea of its weapons.
“It would be foolish to give any of that away early in discussions, given the long North Korean track record of breaking agreements,” said Christine Wormuth, a former top Defense Department policy official in the Obama administration.
Mr. Trump, however, has long argued that America’s military presence is not an asset but a liability — not just in South Korea but in Japan as well. As both countries became wealthy, he said, they should have taken on more of the burden for their defense. During the 2016 presidential campaign, he even suggested that the two nations acquire their own nuclear weapons so they did not have to depend on the American nuclear umbrella.
Grudgingly, Mr. Trump admitted that the troops had kept the peace on the peninsula. But he said they had not prevented the North from acquiring nuclear weapons or menacing its neighbors.
Over the past year, officials said, Mr. Trump has continued to question the need for troops with aides like his former national security adviser, Lt. Gen. H. R. McMaster, and his deputy, Maj. Gen. Ricky L. Waddell.
Before the Winter Olympics in Pyeongchang, when tensions between the United States and North Korea were high, the president broached the idea of withdrawing the dependents of troops from South Korea for security reasons. His chief of staff, John F. Kelly, talked him out of the plan, a former official said, because it would have stoked fears of an imminent military strike against the North.
During that period, tensions flared between the White House and the Pentagon because Mr. Trump’s aides believed the military was dragging its feet in providing the president with options for a limited strike on North Korea.
Now, officials said, the situation was reversed: The Pentagon worries that Mr. Trump will push too swiftly to demilitarize.