WASHINGTON (AP) " The Latest on President Donald Trump and North Korea (all times local):

7:50 p.m.

My nuclear button is bigger " and better " than your nuclear button.

That's the message from President Donald Trump to North Korea's Kim Jong Un.

Trump is tweeting in response to Kim's declaration earlier this week that he has a button for nuclear weapons on his table and the entire U.S. mainland is now within strike range.

Trump asks if someone from Kim's "depleted and food starved regime" can "please inform him that I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!"

Trump does not actually have a nuclear button on his desk. The nuclear "football" is carried by a rotating group of military officers everywhere the president goes.

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4 p.m.

President Donald Trump is sounding open to the possibility of an inter-Korean dialogue after North Korean leader Kim Jong Un made a rare overture toward South Korea in a New Year's address.

But U.S. officials are also voicing skepticism about Kim's intentions and repeating the demand that the North give up its nukes.

Using his derisive nickname for Kim, Trump says: "Rocket man now wants to talk to South Korea for first time. Perhaps that is good news, perhaps not - we will see!"