The U.S. flew the two B-1B Lancer bombers over the peninsula along with South Korean F-15k fighter planes and additional fighters from Japan, which the U.S. military said was the first such nighttime maneuver conducted by the three countries together.
The exercise showed the "strong ability of the alliance against the North Korean nuclear missile threat", the South Korean air force said. The South has taken an increasingly aggressive stance toward the North's belligerence amid back-and-forth threats of war between North Korea and President Donald Trump.
There is no evidence that the hacking attempts were successful, but FireEye assessed that the targeting of electric utilities could be related to increasing tensions between the US and North Korea, potentially foreshadowing a disruptive cyberattack.
However, the South Korean defence ministry has refused to comment about this allegation.
An unusually aggressive approach to the North by Trump, which has included rhetoric hinting at USA strikes and threatening the destruction of North Korea's leadership, has some South Koreans fearful that war is closer than at any time since the Korean War ended in 1953 in a shaky cease-fire, leaving the Korean Peninsula still technically in a state of war.
The U.S. Air Force bombers and the South Korean fighters then conducted a second firing exercise over the Yellow Sea, according to the South Korean Joint Chiefs of Staff.
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Rhee told CNN on Tuesday that the documents stolen included the South Korea-US wartime operational plan and a document that includes procedures to "decapitate" the North Korean leadership.
Tensions between the USA and North Korea have intensified in recent months as the Trump administration has struggled to rein in Kim Jong-un's expanding nuclear and ballistic weapons programme. In a speech at the United Nations in September, the US President accused the North Korean leader Kim of being "on a suicide mission" - while Kim responded by vowing to "tame the mentally deranged US dotard with fire".
The South's Yonhap news agency quoted Lee as saying that 235 gigabytes of military documents were taken.
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. North Korea routinely denies responsibility.
While the attention Wednesday was on air power, upcoming US-South Korea naval exercises could further aggravate tensions.
North Korea has yet to comment on either the bombing drills or the hacking claims.