The United States deployed a B-52 bomber on a low-level flight over its ally South Korea on Sunday, a show of force following North Korea's nuclear test last week.

North Korean leader Kim Jong Un maintained that Wednesday's test was of a hydrogen bomb and said it was a self-defensive step against a US threat of nuclear war.

North Korea's fourth nuclear test angered both China, its main ally, and the United States, although the US government and weapons experts doubt the North's claim that the device was a hydrogen bomb.

The massive B-52, based in Guam and capable of carrying nuclear weapons, could be seen in a low flight over Osan Air Base at around noon (0300 GMT). It was flanked by two fighter planes, a U.S. F-16 and a South Korean F-15, before returning to Guam, the US military said in a statement.

Osan is south of Seoul and 77 km (48 miles) from the Demilitarised Zone that separates the two Koreas. The flight was "in response to recent provocative action by North Korea", the US military said.

In Washington, White House Chief of Staff Denis McDonough said on Sunday the flight underscored to South Korea "the deep and enduring alliance that we have with them".

"Last night was a step toward reassurance in that regard and that was important," McDonough said on CNN's "State of the Union."

He said the United States would continue to work with China and Russia, as well as allies Japan and South Korea, to isolate the North until it lives up to its commitments to get rid of its nuclear weapons.

"Until they do it they'll remain where they are, which is an outcast unable to provide for their own people," McDonough said.

China has publicly supported a denuclearised Korean Peninsula, and the United States will "make sure that they understand that a nuclear North Korea is not a stable scenario", he said.

After the North's last test, in 2013, the United States sent a pair of nuclear-capable B-2 stealth bombers over South Korea. At the time, the North responded by threatening a nuclear attack on the United States.

The United States is also considering sending a nuclear-powered aircraft carrier to waters off the Korean peninsula next month to join a naval exercise with Seoul, South Korea's Yonhap news agency reported without identifying a source. However, US Forces Korea officials said they had no knowledge of the plan.

The two Koreas remain in a technical state of war after their 1950-53 conflict ended in a truce, not a peace treaty, and the United States has about 28,500 troops based in South Korea.

An editorial in the North's Rodong Sinmun newspaper on Sunday called for a peace treaty with the United States, which is the North's long-standing position. "Only when a peace treaty is concluded between the DPRK (North Korea) and the US can genuine peace settle in the Korean Peninsula," state news agency KCNA quoted it as saying.

The United States and China have both dangled the prospect of better relations, including the lifting of sanctions, if North Korea gives up its nuclear weapons.

Earlier on Sunday, KCNA quoted Kim as saying no one had the right to criticise the North's nuclear tests.

"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 US-led imperialists," it quoted Kim as saying.

The North's official name is the Democratic People's Republic of Korea.

"It is the legitimate right of a sovereign state and a fair action that nobody can criticise," he said.

Timing of test

Kim's comments were in line with the North's official rhetoric blaming the United States for deploying nuclear weapons on the Korean peninsula to justify its nuclear programme but were the first by its leader since Wednesday's blast.

The United States has said it has no nuclear weapons stationed in South Korea.

Kim noted the test was being held ahead of a rare congress of its ruling Workers' Party later this year, "which will be a historic turning point in accomplishing the revolutionary cause of Juche", according to KCNA.

Juche is the North's home-grown state ideology that combines Marxism and extreme nationalism established by the state founder and the current leader's grandfather, Kim Il Sung.

KCNA said Kim made the comments on a visit to the country's Ministry of the People's Armed Forces.

South Korea continued to conduct high-decibel propaganda broadcasts across the border into the North on Sunday.

The broadcasts, which include "K-pop" music and statements critical of the Kim government, began on Friday and are considered an insult by Pyongyang. A top North Korean official told a rally on Friday that the broadcasts had pushed the rival Koreas to the "brink of war".

Daily life was mostly as normal on the South Korean side of the border on Sunday. A popular ice fishing festival near the border attracted an estimated 121,300 people on Saturday and 100,000 on Sunday, Yonhap reported.