North Korea views such exercises as rehearsals for invasion, and has responded to other recent drills with a spate of increasingly provocative banned weapons tests.
In recent weeks it has tested what state media described as an underwater nuclear-capable drone, and carried out the launch of an intercontinental ballistic missile.
Officials in Seoul and Washington have warned since early 2022 that North Korea may conduct its seventh nuclear test, with some experts saying it could be imminent.
The United States and the South, meanwhile, have ramped up defence cooperation in light of the growing threats.
"The continuous deployment of major US strategic assets on the Korean peninsula is considered an act to enhance the US determination to defend South Korea and the ability to implement extended deterrence," South Korea's defence ministry said in a statement.
The US B-52H was redeployed to the Korean peninsula on Wednesday about a month after its last deployment, the statement said.
Wednesday's exercise also featured South Korea's advanced F-35A fighter jet, it added.
The North has appeared especially sensitive to air drills in the past, with experts noting its air force is the weakest link in its military.
In March, leader Kim Jong Un ordered the North Korean military to intensify drills in preparation for a "real war", and he recently called for an "exponential" increase in weapons production, including of tactical nukes.
Washington has repeatedly restated its "ironclad" commitment to defending South Korea, including using the "full range of its military capabilities, including nuclear".
South Korea, for its part, is eager to reassure its increasingly nervous public about the US commitment to so-called extended deterrence, in which US military assets, including nuclear weapons, serve to discourage attacks on allies.
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