TOKYO — Secretary of State Rice warned North Korea yesterday that America would use the “full range” of its military powers if Pyongyang launched a nuclear strike on Japan.

As she arrived in Tokyo on the first leg of a mission to galvanize opposition to Kim Jong Il’s regime, Ms. Rice made clear that America would protect its key regional ally against any threat following North Korea’s atomic test.

“I want to make sure that everybody understands that the U.S. will fully act on our defense obligations under the mutual defense treaty,” Ms. Rice said.

“The United States has the will and the capability to meet the full range — and I underscore the full range — of its deterrence and security commitment to Japan.”

Ms. Rice met Prime Minister Abe of Japan, ahead of visits to South Korea, China, and Russia. Her tour is intended to ensure coordinated action in the region over U.N. sanctions against North Korea. Senior Japanese officials, including the foreign minister, Taro Aso, had earlier suggested that Tokyo should consider a major policy reverse by acquiring its own nuclear weapons.

Japan has long held an abhorrence of nuclear weapons, dating back to the atomic bombing of Hiroshima and Nagasaki in World War II.

However, the taboo has gradually eroded since 1998, when Pyongyang test-launched a missile over Japanese airspace. The North Korean nuclear test this month has been greeted with particular concern in Japan.

Japan’s policy is not to have nuclear missiles, develop them, or allow them on Japanese soil. However, some of its leaders have now concluded that they should at least be willing to consider the nuclear option.

Japan has a large nuclear power industry, and it is believed that Japan would be able to build nuclear weapons within a matter of months.

But some believe talk of a nuclear weapon is designed to reassure a nervous public that Japan has options beyond America to defend itself.