The hackers broke into the computer networks of South Korea's defense ministry past year and pilfered classified military documents that detailed military operations in case war broke out on the Korean peninsula, South Korea's state news agency Yonhap reported.
Trump has responded with a series of bellicose statements, prompting a war of words with Pyongyang, which in turn has threatened to shoot US bombers out of the sky and fire missiles into the waters near Guam.
While North Korea was not able to hack USA power companies, there are concerns among some of observers that the regime may attempt to damage the power grid by detonating a nuclear device at a high altitude above the US, triggering an electromagnetic pulse (EMP). Two days previous to that comment the president said on the social media platform that Pyongyang had violated agreements "before the ink was dry, making fools of US negotiators".
The bombers took off from the US Pacific territory of Guam, before entering South Korean airspace and conducting firing exercises over the East Sea and Yellow Sea, South Korea's military said.
"Although I will not comment on intelligence matters or specific incidents related to cyber intrusion, I can assure you that we are confident in the security of our operations plans and our ability to deal with any threat from North Korea", Pentagon spokesman Colonel Robert Manning told reporters.
Reports of reconnaissance on USA utilities follow earlier reports alleging DPRK spies stole a large cache of military documents from South Korea, including a plan to assassinate North Korea's leader, Kim Jong-un.
The Pentagon also declined to comment specifically on reports of the potential breach, but spokesman Col. Robert Manning said on Tuesday that the USA is "confident in the security of our operations plans and our ability to deal with any threat from North Korea".
Lee said that 235 gigabytes of military documents were taken, but the military has yet to identify 80 percent of the documents that were compromised.
Information on South Korea's special forces was also reportedly accessed, as well as important details on significant power plants and military facilities in the South.
During an address to the United Nations General Assembly in September, Mr Trump declared that the U.S. would "totally destroy North Korea" if forced to defend itself or its allies.