Mr Moon told the visiting top US military official that there must be a diplomatic solution to the crisis.
Gen Joseph Dunford said the US priority was diplomacy but he added that it was committed to defending the South against a possible military attack.
The North on Monday said any war could "only be turned into a nuclear war".
Also on Monday, China's commerce ministry issued an order banning a slew of imports from North Korea, in line with additional UN sanctions that were announced earlier this month.
The sanctions were introduced in response to a wave of missile tests and increased military rhetoric from North Korea.
In another development, Ukraine has denied supplying North Korea with rocket engines from one of its factories.
A report in the New York Times suggests that Soviet-era engines made at the Yuzhmash factory in Dnipro (the city known until recently as Dnipropetrovsk) were supplied to the North illegally.