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President Barack Obama said Tuesday that a nuclear-armed North Korea poses a "grave threat" to the world, and he vowed to end a cycle of allowing Pyongyang to create crises and then be rewarded with incentives to back down.

"This is a pattern they''ve come to expect," Obama said. "We are going to break that pattern."

Standing alongside South Korean President Lee Myung-bak in the White House Rose Garden, Obama said they agreed that a new U.N. resolution seeking to halt North Korea''s development of nuclear weapons and ballistic missiles must be fully enforced. The U.N. did not authorize military force to enforce the measures.

Lee said he and Obama agreed that "under no circumstance are we going to allow North Korea to possess nuclear weapons." The communist government already has tested two underground nuclear devices and is believed by U.S. intelligence to possess enough material to make several nuclear bombs.

On Capitol Hill on Tuesday, Pentagon officials told a Senate committee that North Korea''s missiles could hit the United States in as few as three years if the North continues progress on its weapons system.

U.S. officials have said the North Koreans appear to be making preparations for a third nuclear test. North Korea also has said it would regard efforts to enforce U.N. sanctions as an act of war.

Asked by a reporter whether he believes his country is under threat of attack from the North, Lee said, "They will think twice about taking any measures that they will regret. North Korea may wish to do so, but of course they will not be able to."

Obama said that North Korea''s record of threatening other countries and spreading nuclear technology around the world means it should not be recognized as a legitimate nuclear power.

"We will pursue denuclearization on the Korean peninsula vigorously," Obama said. "So we have not come to a conclusion that North Korea will or should be a nuclear power. Given their past behavior, given the belligerent manner in which they are constantly threatening their neighbors, I don''t think there''s any question that that would be a destabilizing situation that would be a profound threat not only to United States'' security but to world security."

Nor will the international community respond to North Korean provocations, such as additional underground nuclear tests, by offering financial incentives, Lee said.

"They will not be able to gain compensation by provoking a crisis," he said.

Lee added that his country, along with the United States, Japan, China and Russia, will seeking new measures designed to compel the North to "irrevocably dismantle all of their nuclear weapons programs." North Korea earlier this year announced that it would no longer hold talks with those five nations.

Obama said it remains possible for North Korea to take a new path, one that could lead it away from international condemnation and toward a more prosperous future.

"Prestige and security and prosperity are not going to come through the path of threatening neighbors and engaging in violations of international law," he said.

North Korea has bargained with other countries for more than a decade about giving up its nuclear program, gaining such concessions as energy and economic aid, and then reneging.

Lee also called on the North Korean government to release two American journalists and one South Korean worker who are jailed in the North.