Kim Jong Un floats high-level talks

• Report: Kim Jong Un said, "We have no reason not to hold the highest-level talks"


• Last week, North Korea's government branded Park's election as fraudulent


• His words follow an offer by Seoul for minister level talks


• Sticking points between the two sides have led to breakdowns in diplomacy in the past

(CNN) -- Kim Jong Un is not officially on speaking terms with South Korean President Park Geun-hye. But on Thursday, in his New Year's address, he said that could change.

Last week, North Korea's government news agency branded Park's election as fraudulent and her father -- himself a former President -- a dictator.

But in his televised speech, for the first time ever, the communist leader said he'd talk with Park, South Korean news agency Yonhap reported.

"Depending on the mood and circumstances to be created, we have no reason not to hold the highest-level talks," Kim said.

North Korea's state news agency did not publish those remarks in the official transcript of Kim's speech.

"We should make fresh headway in the national reunification movement for this year."

Kim Jong-un

His words may represent a small glacial budge, but that doesn't mean things will keep moving, Yonhap cautioned. Still, Kim spoke in detail about the need to improve North-South relations.

Moments of thaw

In between bellicose bantering -- particularly against the South's military partnership with the United States -- there have been momentary thaws. Three months ago, some of the North's highest officials paid a snap friendly visit to the South that sparked excited live television coverage.

And this past Monday, Seoul's unification minister, Ryoo Kihl-jae, sent a fax to Pyongyang suggesting Cabinet ministers on both sides to meet in January, Yonhap reported.

"The South and the North will have to meet each other and discuss ways toward peaceful reunification," Ryoo later told journalists.

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South Korean soldiers stand guard as Christians stage a lighting ceremony in front of a Christmas tree atop a military-controlled hill near the tense land border in Gimpo, west of Seoul, on December 21, 2010. North Korea has objected to Christmas trees at the border since the 1960s.

Cubans watch a South Korean soap opera DVD in Havana, on December 5, 2013. South Korea's National Intelligence Service told lawmakers in October that officials from the North's ruling party had been executed by firing squad for viewing a South Korean soap opera.

South Korean pop group Four Minute perform on stage during the 20th Dream Concert on June 7, 2014 in Seoul, South Korea. An anti-North Korea radio show by the South had opened with a pop song from the quartet.

A picture taken by North Korea's official Korean Central News Agency shows the statues of late leaders Kim Il Sung (third left) and Kim Jong Il (third right) at Mangyongdae Revolutionary School in Pyongyang on February 16, 2013. Photographers who have spent time in the country say that particular care must be taken when snapping pictures of statues of North Korean leaders.

South Korean activists release balloons carrying anti-North Korea leaflets at a park near the border in Paju, north of Seoul, on October 10, 2014. The balloons anger the regime in Pyongyang, drawing regular threats of violent reprisals.

A Catholic worshiper reads from a Bible at the Myeong-dong Cathedral in Seoul on August 6, 2014. Although North Korea has some state-controlled churches, the regime forbids independent religious activities.

The things that annoy North Korea

The things that annoy North Korea

The things that annoy North Korea

The things that annoy North Korea

The things that annoy North Korea

The things that annoy North Korea

The things that annoy North Korea

Both want reunification

Reunification is what both sides are pushing for.

"We should make fresh headway in the national reunification movement for this year," Kim said in Thursday's address, according to the official transcript published by the North's Korean Central News Agency.

But they have pursued it on starkly different terms.

President Park last year announced a 2015 road map to reunification, which she laid out in a speech in April in Dresden, Germany, Yonhap has reported.

Dresden was part of East Germany, back when Germany was divided between the democratic West and Soviet Communist East, and South Koreans have drawn hope from that country's reunification for the possible realization of their own. Park's talk has been called the Dresden Declaration.

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Free market support

Since then, the South has sought support from its international allies for Park's reunification plan, selling a single Korea as an economic boon to a global free market, Yonhap has reported.

The North has railed against this, fearing the economically muscular South, aided by other capitalist countries, would, in a reunification, effectively digest the North. Kim does not want Seoul's allies involved and criticized the South's diplomatic efforts again on Thursday.

"To go on a tour around foreign countries touting for 'international cooperation' in resolving the inter-Korean relations issue, the one related with our nation, is a humiliating treachery of leaving its destiny in the hands of outside forces," he said.

But Kim's conciliatory words following after the South's offer to talk again, and his hints of moving talks up to the highest level could be significant.

Ryoo, who extended that invitation, is also Park's right hand in her reunification effort, Yonhap reported. He said his offer to talk was in line with the 2015 road map.

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Fragile situation

But Kim's speech was not all conciliatory. Some of it was bellicose.

He commended his forces' "showdown with the imperialists," possibly a reference to caustic reactions to South Korean-U.S. military exercises.

The dictator also praised political killings in his own ranks.

"Our Party detected and purged the anti-Party, counterrevolutionary factionalists at an opportune time and with a correct decision," the KCNA speech transcript said.

South Korean intelligence officials said that members of the North's ruling party were shot by firing squad for viewing a South Korean soap opera.

And there are additional pressure points that have derailed Seoul-Pyongyang agreements in the past, such as the floating of messages via balloon by activists in the South into the North. North Korean soldiers opening fire on these balloons last year struck South Korean territory. There were no reported injuries or damage.

The North sees the balloons as a violation of its borders. The South sees them as an exercise of free speech.

The South imposed an economic sanctions package on the North in 2010 over the attack on a South Korean navy ship that killed 46 sailors. Seoul demands that Pyongyang take responsibility for torpedoing the vessel before it lifts the sanctions.