US President Donald Trump has referred to North Korea's leader Kim Jong-un as "Rocket Man" - and pictured himself taking out his former election rival Hillary Clinton with a golf ball.

Trump spoke on Saturday night with South Korea's President Moon Jae-in, pledging joint "steps to strengthen deterrence and defence capabilities and to maximise economic and diplomatic pressure on North Korea", according to the White House.

Trump's account of the conversation, which kicked off an unbridled salvo of early morning tweets on Sunday, struck a less diplomatic tone.

"I spoke with President Moon of South Korea last night. Asked him how Rocket Man is doing. Long gas lines forming in North Korea. Too bad!" the president wrote to his 38 million followers.

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He then launched into half a dozen retweets of internet memes celebrating his Make America Great Again campaign theme - topping it off with a GIF montage of himself taking a swing at a golf ball and knocking out his erstwhile Democratic rival Hillary Clinton.

I spoke with President Moon of South Korea last night. Asked him how Rocket Man is doing. Long gas lines forming in North Korea. Too bad! — Donald J. Trump (@realDonaldTrump) September 17, 2017

A senior Democrat, US representative Adam Schiff, said the retweet was disturbing.

"It is distressing ... to have a president that frankly will tweet and retweet things as juvenile as that," Schiff said on ABC's This Week programme. "It doesn't help; I think in terms of his stature, it doesn't help in terms of the stature of our whole country."