Terrence O'Shaughnessy, a commander under the South Korea-U.S. Combined Forces Command, said that the flight was in response to recent actions by North Korea.
"The United States remains steadfast in its commitment to the defence of the Republic of Korea (South Korea) and to maintaining stability on the Korean Peninsula, to include extended deterrence provided by our conventional forces and our nuclear umbrella. B-52 mission re-enforced the U.S. commitment to the security of our allies and partners and demonstrate one of many alliance capabilities available for the defense of the Republic of Korea."
South Korean Air Force Commander Lee Wang Geun also said that his country will work closely with the U.S.
"Our air force is ready to punish any provocations firmly and strongly whenever, wherever, and in whatever shape it may be. The ROK-US alliance is more steadfast than ever. The ROK-US combined Air Forces is based on the intimate sharing of intelligence and powerful and precise firepower, which will neutralise the enemy's intent for provocation."
The U.S. B-52 bomber conducted a low-level flight over Osan Air Base near South Korean capital Seoul and then returned to its base in Guam on Sunday.
The bomber was armed with a nuclear missile and "bunker buster" bombs.
The flight was also joined by a U.S. F-16 and a South Korean F-15.
It is reported that the bomber is one of the retaliatory measures from the U.S. and South Korea against North Korea.
The two sides are said to be considering more steps including the deployment of U.S. aircraft carrier Ronald Reagan currently in Yokosuka, Japan.
They may also send a U.S. nuclear-powered submarine and F-22 stealth fighter.
Earlier on Sunday, North Korea's state media quoted top leader Kim Jong Un calling the H-bomb test a self-defensive step.
"The DPRK's H-bomb test is a self-defensive step for reliably defending the peace on the Korean Peninsula and the regional security from the danger of nuclear war caused by the U.S.-led imperialists. It is the legitimate right of a sovereign state and a fair action that is above criticism."
According to the official KCNA news agency, the comment was made by Kim during a visit to the Ministry of People's Armed Forces to congratulate on their first H-bomb test.
The announcement triggered international condemnation.
Many experts also expressed suspicion over the country's capability of developing an H-bomb.
They said the 5.1 seismic tremor caused by the test was too small to be caused by a proper hydrogen bomb explosion.
For CRI, this is Fei Fei.
