SEOUL, South Korea — The United States and South Korea vowed on Tuesday to push for the “strongest possible” resolution at the United Nations Security Council, including new sanctions and the removal of existing loopholes, to punish North Korea for its latest nuclear test.

The top American and South Korean envoys on North Korea expressed their resolve during a news conference in Seoul, the South’s capital, on Tuesday, speaking shortly after two nuclear-capable supersonic bombers from the United States Air Force base in Guam streaked over the South in a show of force.

The flight by the B-1B bombers demonstrated the United States’ commitment to providing “extended deterrence,” including the threat of using nuclear weapons, to protect the South, said Gen. Vincent K. Brooks, the top American military commander in the country. It was also intended to help counter calls among nationalist politicians and scholars here who contend that the South must arm itself with nuclear weapons.

On Tuesday, Sung Kim, Washington’s top official dealing with North Korea, and his South Korean counterpart, Kim Hong-kyun, reiterated that the South did not need to build its own nuclear bombs or to reintroduce American tactical atomic bombs that were withdrawn in the early 1990s.