US Defense Secretary Donald Rumsfeld has offered assurance of his country's "firm commitment" and "immediate support" to South Korea, including continuation of the extended deterrence offered by the US nuclear umbrella, a document released by the Pentagon on Saturday said.

Rumsfeld made the pledge in the joint communique of the 38th Security Consultative Meeting between the defense chiefs of the two countries, which was held in Washington on Friday.

Rumsfeld "offered assurances of firm U.S. commitment and immediate support to the ROK (Republic of Korea), including continuation of the extended deterrence offered by the U.S. nuclear umbrella, consistent with the Mutual Defense Treaty," the document said.

The defense secretary and his South Korean counterpart, Defense Minister Yoon Kwang-ung, expressed "grave concern" regarding the nuclear test by the Democratic People's Republic of Korea (DPRK) on Oct. 9.

Rumsfeld and Yoon observed in the document that presidents of the both countries "had reaffirmed the shared principle of a peaceful and diplomatic resolution" of the DPRK nuclear issue and had agreed to seek a common and comprehensive approach for the resumption and progress of the six party talks.