Trump spoke over phone with Moon two days after North Korea fired a missile over Japan.
In a twitter post after the call, Trump referred to North Korea's leader Kim Jong-Un as "Rocket Man".
"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!" Trump said in a tweet.
In a readout later, the White House said the two leaders discussed North Korea's launch of the latest ballistic missile, the second such launch over Japan in less than three weeks.
Trump and Moon committed to continuing to take steps to strengthen deterrence and defence capabilities and to maximise economic and diplomatic pressure on North Korea, it said.
The two leaders noted that they will continue their close consultations when they meet on the margins of the United Nations General Assembly this week, said the White House.