Story highlights South Korean president sees a 'window of opportunity' after Kim Jong Il's death

He offers economic aid to the North if the country gives up its nuclear program

North Korea is refusing to engage with the current South Korean government

Pyongyang describes the current South Korean administration as "traitors"

The South Korean president, Lee Myung-bak, offered Monday to cooperate with North Korea to begin a "new era" of relations between the two countries, a day after Pyongyang had said it would defend its new leader, Kim Jong Un, to the death.

"The most important goal for the country is peace and stability on the Korean peninsula," Lee said in his New Year's address to the nation. He called the transitional period following the North Korean leader Kim Jong Il's death "a window of opportunity."

The president said in a live televised broadcast that the South is prepared to offer economic aid to the North, if Pyongyang is willing to give up its nuclear program. But he emphasized that Seoul will keep up its guard against any aggression from its unpredictable neighbor.

Lee's remarks may fall on deaf ears in Pyongyang, which has recently directed a barrage of invective at his government.

North Korea published a New Year's editorial Sunday in which it described the 28,500 U.S. troops stationed in South Korea as the main obstacle to peace on the peninsula.

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The editorial also called the South Korean government "traitors" for not allowing more citizens to visit the North to pay respects to Kim Jong Il, who died on December 17.

Kim's elaborate funeral and memorial service, held by the North last week, appeared to cement the position of Kim Jong Un, his son and chosen successor, as the country's new "supreme leader."

But the change in leadership has not so far brought any signs in a change in the regime's stance toward South Korea.

The North Korean state-run media KCNA on Friday quoted a National Defense Commission statement saying that Pyongyang would have "no dealings" with Lee's government.

During his address Monday, Lee also warned South Koreans of the looming economic struggles in 2012, saying the government will place a great emphasis on stabilizing consumer prices in the new year.

South Korea will invest 10 trillion won, roughly $8.6 billion, in creating new jobs, Lee said, promising to increase welfare support for families with young children to combat the low birth rate in an aging society.