Rhee Cheol-Hee, a lawmaker for the ruling Democratic party, said the hackers had broken into the South's military network last September and gained access to 235 gigabytes of sensitive data, the Chosun Ilbo daily reported.
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.
Rhee, a member of parliament's defence committee, could not be reached for comment but his office said he had been quoted correctly.
In his latest tweet over the weekend, Trump reiterated that diplomatic efforts with North Korea have consistently failed, adding that "only one thing will work".
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Citing Seoul's defence ministry, Rhee said that 80 percent of the leaked documents had yet to be identified.
But the contingency plan for the South's special forces was stolen, he said, as well as details about annual joint military drills with the US and information on key military facilities and power plants.
In May the ministry said North Korea had hacked into Seoul's military intranet but did not say what had been leaked.
Pyongyang has a 6,800-strong unit of trained cyber- warfare specialists, according to the South Korean government. It has been accused of launching high-profile cyber-attacks including the 2014 hacking of Sony Pictures.
The Chosun Ilbo story was the second report today of military-related cyber-attacks in the Asia-Pacific.
Australia's government said separately an unidentified defence contractor had been hacked and a "significant amount of data" stolen.
There were 47,000 cyber-incidents in the last 12 months, a 15 percent increase from the previous year, Minister for Cyber Security Dan Tehan said in Canberra as he launched a report by the Cyber Security Centre
The Australian newspaper reported that the hacker was based in China but Tehan told the Australian Broadcasting Corporation that "we don't know and we cannot confirm exactly who the actor was".
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