South Korea's President Lee Myung-Bak said Monday the divided peninsula is at a turning point after the death of North Koreanleader Kim Jong-Il, with opportunities to improve relations.

But Lee also vowed to hit back hard against any provocations from the North under the leadership of its young new chief Kim Jong-Un, son of the late dictator.

Pyongyang kept up a barrage of criticism of the conservative South Korean leader's government, telling them to "apologise on their knees" for alleged insults during the 13-day mourning period for Kim.

Lee, in a televised New Year address, said the peninsula's political situation "is at a turning point. But there are new opportunities in the changes and uncertainties."

"We are leaving the window of opportunity open. We will be able to open the door for a new era in the Korean peninsula if North Koreashows sincerity," he added.

The North has stressed continuity since longtime leader Kim Jong-Il's death on December 17 and Jong-Un's elevation as "great successor".

Last week it warned the world to expect no policy changes under the son, and threatened unspecified retaliation against the South for its perceived disrespect to the late Kim.

Seoul expressed sympathy to the North's people but not its regime over Kim's death and allowed just two private mourning delegations to visit Pyongyang. It did not send an official delegation.

Lee said the South "will respond strongly" to any aggression but also raised the prospect of "big changes" following the death.

He said he hoped 2012 would be a milestone in years-long efforts to negotiate an end to the North's nuclear weapons programmes.

Six-nation talks could resume as soon as Pyongyang halts its atomic activities, he said, but did not elaborate further on what possible changes lay in store for the Korean peninsula.

Policymakers are waiting to see whether the untested Jong-Un, aged in his late 20s, will be a forceful leader of a nation with the world's fourth-largest military, or a figurehead for powers behind the throne.

Some analysts see the possibility of border attacks to try to bolster support for the new dynastic leader against a perceived external enemy.

"We... will never tolerate the inhuman crime committed by Lee Myung-Bak's regime and will fight till the end if they do not apologise on their knees," the North's party newspaper Rodong Sinmun said on Monday.

Pyongyang has already vowed never to deal with the government of Lee, who under the constitution must end his term in February 2013.

On Saturday it threatened to "settle accounts" unless Seoul apologises for the alleged insults during the mourning period.

Cross-border ties have been frosty since Lee took office in February 2008 and scrapped his liberal predecessors' policy of near-unconditional aid and engagement with the North.

Relations turned icy when the South accused the North of torpedoing a warship in March 2010 with the loss of 46 lives.

The North denied involvement but killed four South Koreans in an artillery attack on a border island in November 2010.

On Sunday, in a state newspaper editorial setting policy for 2012, the North urged its military to become "human rifles and bombs" to defend Jong-Un and to rally behind him.

It called for a nationwide struggle against what it termed the hostile and confrontational policy of "traitors" led by Lee.