The May 3 gunfire exchange was the first shooting inside the Korean Demilitarized Zone in about 2½ years.
Courtesy patrols by military police have been standard practice for years.
North Korea said U.S. pressure had nothing to do with its peace overtures to the U.S. and South Korea.
It is unclear whether U.S. aircraft carriers and nuclear submarines would participate as they have in previous war games.
The U.N. Command said in a statement it was investigating if there was a violation of an armistice that ended the Korean War.
The exchange of gunfire comes after Kim Jong Un had made his first public appearance in nearly three weeks.
As the absolute leader of a country with a nuclear weapons program, Kim's health is matter of intense interest.
Army Spc. Deontae Chappel was "shocked" but not overly worried when he found out he had the respiratory disease in February.
At least eight base barbershops and three fitness centers reopened Saturday.
The first soldier has been released after 49 days in isolation in South Korea.