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.
South Korean and U.S. government officials "have been raising their guard against more North Korean provocations with the approach of the 72nd anniversary of the founding of North Korea's ruling party", says Reuters.
Trump and North Korean leader Kim Jong-un exchanged heated rhetoric in recent weeks.
"If I had access to the enemy's plans, not only would I know what forces were going to be arrayed against me, I would know where they will be, what weapons they will have, where the command and control nodes will be established - all critical war-fighting information".
The South Korean Defence Ministry's official stance is that they cannot confirm anything the lawmaker said in terms of the hacked content due to the sensitivity of the matter. The South Korean defence ministry has so far refused to comment on the breach, which reportedly dates back to last September.
They staged a simulated air-to-ground missile firing drill with two F-15K fighters over the East Sea and flew across the peninsula, Yonhap news agency reported.
It was part of a "regular deployment training" aimed at enhancing the capability of implementing the "extended deterrence" against the North, the JCS said.
China, North Korea's closest ally, has suggested that Pyongyang freeze its nuclear missile development while the U.S. stop conducting military exercises with the South that raise fears in North Korea. Some military experts believe that power supply problems make it hard for North Korea to turn on its air defense radars for 24 hours a day and also that the systems might struggle to effectively track advanced warplanes such as B-1Bs, which have low radar-cross sections.
South Korea's Joint Chiefs of Staff say the bombers flew from Anderson Air Force base in Guam and entered the Korean Air Defense Identification Zone at around 8:50 p.m.
North Korea has said Trump is "on a suicide mission" against it, with the country's foreign minister calling the US President "mentally deranged" in a speech at the United Nations last month.
"There is an urgent need for the military to change and update parts that were stolen by North Korea", Lee said.