WASHINGTON - US?President Barack Obama on Tuesday said that the United States remains steadfast in its defense commitments to the Republic of Korea (ROK), including the extended deterrence offered by the US nuclear umbrella in his phone call with Republic of Korea President Lee Myung-bak.

Obama spoke to ROK President Lee Myung-bak this morning to consult and coordinate on the response to the announced nuclear test of the Democratic People's Republic of Korea (DPRK). The two leaders condemned this "highly provocative" violation of DPRK's international obligations, the White House said in a statement on Tuesday.

They agreed to work closely together, including at the United Nations Security Council, to seek a range of measures aimed at impeding DPRK's nuclear and ballistic missile programs and reducing the risk of proliferation, noted the statement.

Obama also thanked President Lee for his leadership and friendship over the past four years and pledged to work closely with President-elect Park Geun-hye to further strengthen US-ROK cooperation.

Earlier on Tuesday, Obama condemned the nuclear test conducted Tuesday by the DPRK as "highly provocative," while urging for " further swift and credible action" by the international community.

The test, which the DPRK claimed as successful, was carried out at 11:57 a.m. local time (0237 GMT) in the Kilju County, North Hamkyung Province.