South Korea has offered to hold high-level talks with rival North Korea next week to discuss cooperation during next month's Winter Olympics and potential improvement in overall ties.

Tuesday's offer came a day after North Korean leader Kim Jong Un said in his New Year's address that he was willing to send a delegation to the Pyeongchang Winter Olympics, which are set for Fe. 9-25 in South Korea.

But the prospect of a North Korean team at the Winter Games drew a blistering response Monday from U.S. Sen. Lindsey Graham, R-S.C., who proposed that if North Korea attends the Olympics, then the United States should not.

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"Allowing Kim Jong Un’s North Korea to participate in #WinterOlympics would give legitimacy to the most illegitimate regime on the planet. I’m confident South Korea will reject this absurd overture and fully believe that if North Korea goes to the Winter Olympics, we do not."

In 2014, Graham also pitched a boycott of the Winter Olympics in Sochi, Russia, objecting then to the prospect of Moscow offering asylum to NSA whistleblower Edward Snowden, Fox News reported.

Kim said Monday that he was “open to dialogue” with Seoul, Reuters reported. However, the North Korean leader also touted his country as a nuclear power, the report said.

Analysts say Kim may be trying to drive a wedge between South Korea and its ally, the United States, as a way to ease international isolation and sanctions against North Korea.

One doesn’t need to be a genius to see that this is what North Korea does: After having created a war-like, crisis atmosphere, (Kim) takes a small step back and there’s a collective sigh of relief that there’s no war. It does wonders for North Korea’s image.”
— Sung-Yoon Lee, Tufts University Fletcher School professor and North Korea expert.

Sung-Yoon Lee, a Tufts University Fletcher School professor and North Korea expert, told the Boston Herald that over the last 25 years the U.S. and its allies “have a less well-developed game plan and no real strategy.”

He said Kim’s actions “paint (President Donald) Trump further into the corner as the aggressor.”

U.S. Sen. Lindsey Graham, R-S.C. (Associated Press)

“One doesn’t need to be a genius to see that this is what North Korea does: After having created a war-like, crisis atmosphere, (Kim) takes a small step back and there’s a collective sigh of relief that there’s no war. It does wonders for North Korea’s image,” Lee said.

Cho Myoung-gyon, South Korean Unification Minster, said the South proposes that the two Koreas meet at the border village of Panmunjom.

The Associated Press contributed to this report.