The three carriers will be likely together in the drills around Monday, according to a South Korean military official, who didn't want to be named, citing office rules.
The soldier took cover behind a South Korean structure within the Joint Security Area (JSA) inside the demilitarised zone between the two Koreas and was later rescued by South Korean and USA soldiers at the border, the United Nations Command (UNC) said in a separate statement.
There was no exchange of gunfire between the two sides, but the South's military said it has raised its level of alertness against any North Korean provocations.
"His organs are extremely damaged... we do not know how long he can hold up", Lee said, describing the soldier's condition as "very serious". From January to August 2017, 780 North Koreans escaped to South Korea, according to officials in Seoul.
Over the decades since the peninsula was divided, dozens of North Korean soldiers have fled to the South through the DMZ, which extends for two kilometers either side of the actual borderline.
The fact that the defector drove to the frontier suggests he may not have been a member of the elite corps of North Korean troops posted to Panmunjom, who are carefully vetted and selected for their loyalty.
Monday was the first time since 2007 a North Korean soldier had defected across the JSA. They stand only several yards away from tall South Korean soldiers wearing aviator sunglasses and standing motionless like statues.
The North's official media hasn't reported about the case, but it previously accused of Seoul of kidnapping or enticing its citizens to defect.
The Joint Security Area was the site of some bloodshed during the Cold War but there hasn't been major violence there in recent years. The attack prompted Washington to fly nuclear-capable B-52 bombers toward the DMZ in an attempt to intimidate North Korea. South Korea said the 12 women, and one man, had chosen to defect to the South.
Moon asked the Chinese leader to reciprocate his scheduled visit with a trip to South Korea during the 2018 PyeongChang Winter Olympic Games in South Korea in late February.
The Associated Press contribute to this report.