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* Obama speaks with South Korea's Lee
* North Korea gave U.S. notice, but not timing (Updates with Obama talk with Lee, details)
By Roberta Rampton and Tabassum Zakaria
WASHINGTON, Feb 12 (Reuters) - U.S. President Barack Obama called a nuclear test on Tuesday by North Korea a "highly provocative act" and said Pyongyang's "threatening activities" warranted action by the international community.
Obama was expected to mention North Korea in his State of the Union speech Tuesday night, but the president would not give any hints about the content.
"We'll find out everything I've got to say tonight," he told reporters who gathered to watch him walk from the Oval Office around the Rose Garden at midday.
Just hours before the 9 p.m. EST address, a televised speech viewed by millions of Americans that lays out his priorities for the coming year, Obama was occupied with the fallout from the third North Korean nuclear test.
Obama spoke with South Korean President Lee Myung-bak and they agreed to cooperate to address North Korea's nuclear program.
"They agreed to work closely together, including at the United Nations Security Council, to seek a range of measures aimed at impeding North Korea's nuclear and ballistic missile programs and reducing the risk of proliferation," the White House said in a statement.
U.S. intelligence agencies were analyzing the event and found that North Korea probably conducted an underground nuclear explosion with a yield of "approximately several kilotons," the Office of the Director of National Intelligence said in a statement.
North Korea had advised the U.S. State Department of its intention to test a nuclear device prior to Tuesday's underground explosion but had not said when it would conduct the test, State Department spokeswoman Victoria Nuland said.
She said the notice came through the "usual channel" but declined to say exactly when Washington received the notification. This usually refers to an office in New York where phone messages and faxes are exchanged between the two countries, which do not have diplomatic relations.
Secretary of State John Kerry had telephone conversations with his counterparts in Japan and South Korea, both U.S. allies, and with North Korea's ally, China, she said. He was trying to reach Russian Foreign Minister Sergei Lavrov, who was traveling in South Africa, Nuland said.
In an early-morning statement, Obama said the North Korean nuclear test was "a highly provocative act" that undermined regional stability and violated United Nations and other international agreements.
"The danger posed by North Korea's threatening activities warrants further swift and credible action by the international community. The United States will also continue to take steps necessary to defend ourselves and our allies," Obama said.
North Korea is banned under U.N. Security Council resolutions from developing nuclear and missile technology. The tests drew condemnation from around the world.
"North Korea's nuclear weapons and ballistic missile programs constitute a threat to U.S. national security and to international peace and security," Obama said. "The United States remains vigilant in the face of North Korean provocations and steadfast in our defense commitments to allies in the region," he said.
"These provocations do not make North Korea more secure," Obama said. "Far from achieving its stated goal of becoming a strong and prosperous nation, North Korea has instead increasingly isolated and impoverished its people through its ill-advised pursuit of weapons of mass destruction and their means of delivery," he said.
The magnitude of the test was roughly twice as large as that of 2009, said Lassina Zerbo, director of the international data center division of the Vienna-based Comprehensive Nuclear-Test Ban Treaty Organization. The U.S. Geological Survey said that a seismic event measuring 5.1 magnitude had occurred. (Additional reporting by Jeff Mason, Paul Eckert, and Susan Heavey; Editing by Cynthia Osterman)