This will mark the first U.S. visit for Moon, who took office last month after the previous president was impeached on corruption charges.
North Korea is likely to be discussed as the two leaders have differing policies. Moon has supported engagement with the largely isolated country. Trump, however, said that North Korea "is a big problem" that needs to be solved. Previous South Korean presidents have taken more hardline stances against North Korea, lining closer with Trump's views.
Moon and Trump also met for dinner Thursday evening.
"We're going to have tremendous discussions tonight," Trump said at the dinner. "I know you've been discussing with our people some of the complexities of North Korea and trade and other things, and we’ll be discussing them all as we progress — and it could be very well late into the evening."