Donald Trump in childish Twitter exchange with Korea's Kim

US President Donald Trump has started a school yard taunts exchange with North Korea's leader Kim Jong Un in a response to North Korea calling Trump's speech in South Korea "reckless remarks by an old lunatic."

In a Tweet on Sunday morning, Trump wrote:

Why would Kim Jong-un insult me by calling me 'old,' when I would NEVER call him 'short and fat?

Trump goes on to say sarcastically,

Oh well, I try so hard to be his friend - and maybe someday that will happen!

Why would Kim Jong-un insult me by calling me "old," when I would NEVER call him "short and fat?" Oh well, I try so hard to be his friend - and maybe someday that will happen!

— Donald J. Trump (@realDonaldTrump) November 12, 2017

Trump has been working to rally global pressure against North Korea's nuclear weapons program on a trip to Asia.

That includes a stern speech delivered in South Korea's National Assembly on Tuesday, in which he said: 

Do not underestimate us. And do not try us. ... The weapons you're acquiring are not making you safer, they are putting your regime in grave danger. Every step you take down this dark path increases the peril you face.

On Saturday, Kim's government accused Trump of trying to demonise North Korea.

Reckless remarks by an old lunatic like Trump will never scare us or stop our advance," the North's Foreign Ministry said in a statement.

On the contrary ... it pushes us to speed up the effort to complete our nuclear force.