The U.S. ambassador to the United Nations, Nikki Haley, has raised concerns about the safety of American athletes at the Games, although the White House later said that they would attend.
South Korean President Moon Jae-in said he had asked the U.S. military to postpone the joint military exercises until after the Olympics, and the U.S. command in Seoul said it was considering the request.
"It is possible for South Korea and the U.S. to review the possibility of postponing the drill," Moon told NBC News in an interview Tuesday, adding that a delay was contingent on North Korea not conducting any more missile or nuclear tests.
"I have made such a suggestion to the U.S., and the U.S. is currently reviewing. It all depends on how North Korea behaves," Moon said.
An official at the president's residence, the Blue House, clarified those remarks Wednesday, saying the allies would delay the exercises only for the duration of the Games. The Paralympics finish March 18.
Separately, a North Korean soldier escaped across the Demilitarized Zone into South Korea early Thursday morning, prompting warning shots to be fired from both sides. The soldier appeared in front of a guard post on the southern side shortly after 8 a.m. local time, the South's military said, and North Korean border guards came looking for him.
This follows the high-stakes defection of another North Korean soldier through the DMZ last month.
Each spring, the U.S. and South Korean militaries conduct huge field and computer-based exercises to train for a potential conflict with North Korea or the collapse of the regime there.
The dates for next year's exercises have not been announced, but the Key Resolve computer-simulated command post exercise was held March 8-23 this year, while the Foal Eagle field training exercises began March 1 and continued through the end of April.
About 17,000 American and more than 300,000 South Korean troops participated in the exercises, which included drills to preemptively "detect, defend, disrupt and destroy" North Korean nuclear and missile facilities.
The two militaries have been doing winter training exercises this month at PyeongChang, the site of the Winter Olympics, including ski combat drills in temperatures that have fallen to minus-4 degrees Fahrenheit.
"Both the U.S. Marines and the [South Korean] marines have covered over-the-snow ability," U.S. Marine Capt. Thomas Rigby told reporters in PyeongChang this week. "We've covered reconnaissance skills as well as critical combat skills in a cold-weather mountainous environment."
The winter training exercises finish Friday.
The proposal to delay the spring training exercises "is limited to holding the Olympic Games peacefully," the unnamed South Korean official told local reporters.
"Because the Olympics is an international event and the North Korean nuclear issue is creating a global crisis, it is only natural that we make efforts to find a solution [to the North Korea issue] through the Olympic Games if we must," the official said, according to the Yonhap News Agency.
The U.S. military command in Korea said it also wants to ensure a successful Olympics.
"We, as allies, are committed to an alliance decision on the exercises and will announce the decision when appropriate," it said in an emailed statement.
North Korea has conducted more than 25 missile launches this year and detonated a huge nuclear device in September, leading to widespread international condemnation.
The government in Seoul worries that Pyongyang may try to disrupt the Olympics, and ticket sales have been disappointing. North Korea has not committed to sending any athletes to the Games, although a figure-skating pair has qualified to compete.
South Korea plans to deploy about 5,000 troops to the Games, double the number dispatched during the 2002 soccer World Cup.
Every year, North Korea vehemently denounces the joint military exercises as a pretext for an invasion.
After this year's Key Resolve and Foal Eagle drills, the North's Rodong Sinmun newspaper described the effort as "unprecedentedly provocative and dangerous confrontational hysteria in view of its scale, program and purpose."
In a commentary, the paper — the mouthpiece of the ruling Workers' Party — said the exercises showed that a nuclear war may erupt on the Korean Peninsula any moment.
"War has not yet broken out on the peninsula, the world's biggest hotspot," it said, adding that this was entirely because of North Korea's nuclear deterrent.