Sung, also a member of the parliament’s national defence committee, said the jamboree had “tarnished our country’s reputation due to inadequate preparation and poor management”.
The defence ministry told AFP that it had “nothing to comment” on Sung’s request.
About 43,000 people had gathered on South Korea’s coast last week for the World Scouts Jamboree.
But it was plagued by problems, initially with a heatwave that led to mass sunstroke casualties. Poor sanitation was another problem.
An approaching typhoon led organisers to scrap the campsite proceedings completely this week.
Thousands of students were being evacuated to Seoul and other parts of the country on Tuesday.
Even before the typhoon warning, Korean media had called the jamboree “a national disgrace”.
But Sung’s request prompted angry responses from some BTS fans online.
“Please don’t use BTS to cover yourselves up!” one wrote on Twitter, which is now being rebranded to X.
“Isn’t it absurd that (the South Korean authorities) are putting the responsibility on BTS to clean up the mess they produced – by not adequately preparing for the Jamboree?” wrote another.
BTS has played a significant role in promoting South Korea’s culture, once even serving as the country’s presidential envoy.
Last year, they threw a free concert in Busan in support of South Korea’s bid to host the World Expo 2023 in the southern port city.
It was their last concert as a group before the members started joining the army for mandatory military service.