SEOUL, South Korea — The American military made a rare announcement that two nuclear-capable B-2 stealth bombers ran a practice bombing sortie over South Korea on Thursday, underscoring Washington's commitment to defend its ally amid rising tensions with North Korea.

The two B-2 Spirit bombers made a nonstop round trip from Whiteman Air Force Base in Missouri, demonstrating the United States' ability to "provide extended deterrence to our allies in the Asia-Pacific region" and to "conduct long-range, precision strikes quickly and at will," the American command in the South Korean capital, Seoul, said in a statement.

It was the first time the American military publicly confirmed a B-2 mission over the Korean Peninsula. As the bombers dropped inert munitions that they carried 6,500 miles over the Pacific to an island bombing range off South Korea's west coast, Secretary of Defense Chuck Hagel conferred with his South Korean counterpart, Kim Kwan-jin, on the phone, reaffirming the United States' "unwavering" commitment to defend the South.

After suffering from the American carpet-bombing during the 1950-53 Korean War, North Korea remains particularly sensitive about American bombers. It keeps most of its key military installations underground and its war cries typically reach a frenetic pitch when American bombers fly over South Korea during military exercises. The resulting fear and anti-American sentiment is used by the regime to make its people rally behind the North's "military-first" leadership.

Both B-52 and B-2 can launch nuclear-armed cruise missiles. The Pentagon used their training sorties over the Korean Peninsula to highlight the role the long-distance strategic bombers play as part of Washington's "nuclear umbrella" over South Korea and Japan. In South Korea, North Korea's successful launching of a three-stage rocket in December and its nuclear test last month were unsettling enough that several right-wing politicians began calling on their government to build nuclear arms.

A news release from the South Korean Defense Ministry on Thursday said that the "extended deterrence" Mr. Hagel reaffirmed for South Korea included "nuclear umbrella" and "missile defense capabilities."

The allies also agreed to develop "customized" plans to deal with various types of threats posed by North Korea's nuclear and other weapons of mass destruction, it said.

North Korea has escalated its bellicose rhetoric since a Feb. 12 nuclear test. It threatened pre-emptive nuclear strikes against the United States and South Korea for conducting joint military drills and supporting United Nations sanctions against the North. In response, Washington has stood behind the new government of President Park Geun-hye, South Korea's first female president, by running B-52 bomber sorties over South Korea earlier this month and publicizing them. It also signed an agreement last weekend to enhance consultation and coordination of the allies' responses to North Korean provocations. Such coordination became all the more important with growing North Korean threats; under a mutual defense treaty, Washington is obliged to intervene should a local skirmish expand into a full-blown war.

The Pentagon said the B-52 and B-2 training missions were part of its Foal Eagle joint military drill with South Korea, which began on March 1 and will run through April 30. North Korea cited the threat of B-52 bombers when it cut off its last remaining military hot lines with South Korea on Wednesday and warned of more "substantial military actions." The military hot lines have been used to allow South Korean workers and cargo traveling to a joint industrial park in the North Korean town of Kaesong to clear a border crossing. The cross-border traffic operated normally on Thursday. About 420 South Korean commuters from Seoul entered Kaesong and 400 returned to Seoul as North Korea gave them a travel permit through an economic liaison office in Kaesong and the North Korean military did not stop them.

The Kaesong complex, which is an important source of income for the financially struggling North Korean government, has survived years of military tensions and United Nations sanctions. In Kaesong, 123 South Korean companies employ 53,400 North Korean workers for an average monthly pay of $144. They produced $470 million worth of textiles and other labor-intensive goods last year. The fate of Kaesong is seen as a key test of how far North Korea will take its threats.