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

U.S. President Barack Obama and South Korean President Lee Myung-bak are seen during their joint news conference in the Rose Garden of the White House in Washington on Tuesday. (Pablo Martinez Monsivais/Associated Press)"This is a pattern they've come to expect," Obama said. "We are going to break that pattern."

With South Korean President Lee Myung-bak at his side in the White House Rose Garden, Obama said they agreed that a new UN resolution seeking to halt North Korea's development of nuclear weapons and ballistic missile must be fully enforced. The UN 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."

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 nuclear power.

"We will pursue denuclearization on the Korean peninsula vigorously," Obama said.

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," Lee said.

North Korea has bargained with other countries for more than a decade to give up its nuclear program, gaining such concession as energy and economic aid, and then reneging on terms of the agreements.

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