"Through the exercise, the South Korean and US air forces have demonstrated the alliance's strong will and capability for strong retaliation against North Korea's nuclear and missile threats", the South Korean military said in the statement, adding that the exercise also improved the two air forces' readiness to deploy "a rapid response force".
The bombers were dispatched from Andersen Air Force Base in Guam and flew over the Korean peninsula, reportedly staging simulated bombing drills while flying in formation with around 20 aircraft participating in the annual "Vigilant Ace" air combat drill.
"We hope all relevant parties can maintain calm and restraint and take steps to alleviate tensions and not provoke each other", he said.
U.S. military drills on the Korean Peninsula were always a fairly common occurrence, and one which fuels a lot of tension.in the region.
But even though both sides make overtures toward war, it's far from a sure thing.
The warplanes simulated land strikes at a military field near South Korea's eastern coast. The U.N. did not offer detail as to the subject of the talks, but Feltman is expected to also meet foreign minister Ri and U.N. staff based in the country, the Associated Press reported.
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North Korea said that further escalation through joint drills "will only invite more bad retaliation and precipitate their self-destruction".
He said: "We do not wish for a war but shall not hide from it".
North Korea's foreign ministry blamed the drills and "confrontational warmongering" by U.S. officials for making war inevitable.
While B-1Bs are no longer equipped to carry nuclear weapons of their own, they would be key to any strike targeting major North Korean facilities, he said.
United States national security adviser H.R. McMaster said at the weekend the possibility of war was "increasing every day".
United Nations political affairs chief Jeffrey Feltman arrived in Pyongyang for a four-day visit Tuesday, the first time a high-ranking United Nations official visited the country since 2012.
China and Russian Federation had proposed the USA and South Korea stop major military exercises in exchange for North Korea halting its weapons programmes. Feltman held talks with deputy foreign minister Pak Myong Gun on Wednesday.