Trump and North Korean leader Kim Jong Un have been engaged in an increasingly bellicose exchange of rhetoric, with Trump suggesting the military option was the only way to halt the North's missile and nuclear programmes.
The contents of about 80 percent of the data have not yet been identified, Yonhap reported, citing Rhee, adding that the hack took place in September previous year.
Among the leaked documents was Operational Plans 5015 for use in case of war with the North and including procedures for "decapitation" attacks on leader Kim Jong-Un, the paper quoted Rhee as saying.
The British plans emerged as South Korea was getting ready to build a "blackout bomb", a non-lethal graphite weapon that could destroy North Korea's electricity grid when dropped, Yonhap news agency reported.
Also among them were contingency plans for the South's special forces, reports to allies' top commanders, and information on key military facilities and power plants, he added.
The new weapon is being developed under South Korea's Kill Chain pre-emptive strike program, an initiative exclusively aimed to detect and intercept missiles from North Korea within the shortest time.
It has resulted in an ongoing war of words between Donald Trump and Kim Jong Un.
In response to the unilateral closure, the DPRK kicked out all remaining South Korean people there and announced the freeze and liquidation of all assets inside the zone.
"As sanctions bite further and North Korea becomes more desperate for foreign currency, they will get more aggressive and continue to come after the finance sector".
Under their mutual defense treaty, the United States takes operational control of South Korean troops in the event of war on the divided Korean Peninsula.
However, the South Korean defence ministry has refused to comment about this allegation. It attacked its computer servers with traffic that choked off internet access.