A B-52 bomber flew over South Korea on Sunday, a clear show of force as the rift between Seoul and North Korea have deepened even further following Pyongyang’s fourth nuclear test.

North Korea will surely see the flyover as a clear threat as Pyongyang links its own pursuit of atomic weapons to what it sees as past nuclear-backed moves by the U.S. to topple its authoritarian government. The B-52 was joined by South Korean F-15 and U.S. F-16 fighters and returned to its base in Guam after the flyover, the U.S. said.

"This was a demonstration of the ironclad U.S. commitment to our allies in South Korea, in Japan, and to the defense of the American homeland," said Adm. Harry B. Harris Jr., commander U.S. Pacific Command, in a statement. "North Korea's nuclear test is a blatant violation of its international obligations."

The warplanes’ flight follows a victory tour by North Korean leader Kim Jong Un to celebrated the country’s purported claim of a hydrogen bomb test. Kim is seeking to rally nationalistic pride as the rest of the world is outraged over reports or the test.

Kim defended the nuclear test on Sunday, calling the explosion “a self-defensive step” meant to protect the region “from the danger of nuclear war caused by U.S.-led imperialists,” according to a news dispatch from the state-run Korean Central News Agency.

"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," KCNA quoted Kim as saying, according to Reuters.

Kim’s comments shed light into North Korea’s long-running argument that it is the presence of tens of thousands of U.S. troops in South Korea and Japan, and a “hostile” U.S. policy that seeks to topple the Pyongyang government.

During his tour, Kim posed for photos with leading military officials in front of statues of the two members of his family who led the country previously — Kim Jong Il and Kim Il Sung. He also sought to link the purported success of the nuclear test to a ruling Workers' Party convention in May, the party's first since 1980. He's expected to use the congress to announce major state policies and shake up the country's political elite to further consolidate his power.

World powers are looking for ways to punish the North over a nuclear test that, even if not of a hydrogen bomb, still likely pushes Pyongyang closer to its goal of a nuclear-armed missile that can reach the U.S. mainland. Many outside governments and experts question whether the blast was in fact a powerful hydrogen test.

 South Korea has retaliated to the nuclear test by resuming its anti-Pyongyang propaganda from huge speakers along the border. North Korea is reportedly using its own speakers to drown out the noise to keep its soldiers from hearing the South Korean messages.

The North Korean ruling party warned Saturday that the South’s actions are pushing the peninsula to the “brink of war.” North Korea considers the South Korean broadcasts tantamount to an act of war. When Seoul Korea briefly resumed propaganda broadcasts in August after an 11-year break, Seoul says the two Koreas exchanged artillery fire.

South Korea's Yonhap news agency said Seoul had deployed missiles, artillery and other weapons systems near the border to swiftly deal with any possible North Korean provocation. The ministry would not confirm the report, nor another by Yonhap that said North Korea had started its own broadcasts likely meant to keep its soldiers from hearing the South Korean messages.

Officials say broadcasts from the South's loudspeakers can travel about 6 miles during the day and 15 miles at night. That reaches many of the huge force of North Korean soldiers stationed near the border, as well as residents in border towns such as Kaesong, where the Koreas jointly operate an industrial park that has been a valuable cash source for the impoverished North.

While the South's broadcasts also include news and pop music, much of the programming challenges North Korea's government more directly.

"We hope that our fellow Koreans in the North will be able to live in a society that doesn't invade individual lives as soon as possible," a female presenter said in parts of the broadcast that officials revealed to South Korean media. "Countries run by dictatorships even try to control human instincts."

Marathon talks by the Koreas in August eased anger and stopped the broadcasts, which Seoul started after blaming North Korean land mines for maiming two soldiers. It might be more difficult to do so now. Seoul can't stand down easily, some analysts say, and it's highly unlikely that the North will express regret for its nuclear test, which is a source of intense national pride.

Responding to the North's bomb test, U.S. Secretary of State John Kerry urged China, the North's only major ally and biggest aid provider, to end "business as usual" with North Korea.

Diplomats at a U.N. Security Council emergency session pledged to swiftly pursue new sanctions. For current sanctions and any new penalties to work, better cooperation and stronger implementation from China is seen as key.

It may take weeks or longer to confirm or refute the North's claim that it successfully tested a hydrogen bomb, which would mark a major and unanticipated advance for its still-limited nuclear arsenal.

The Associated Press contributed to this report.