WATCH: Trump Becomes First Sitting President to Cross DMZ In Meeting With Kim Jong Un

After days of speculation -- and optimistic statements by the two leaders -- President Trump and North Korean leader Kim Jong Un met and shook hands Sunday at the Demilitarized Zone between North and South Korea.

It was their first face-to-face meeting since an ill-fated summit in Hanoi, Vietnam, in February.

[...] "I was proud to step over the line," Trump told Kim later, inside the Freedom House on the South Korea side, according to the Associated Press. "It is a great day for the world."

Kim appeared pleased by the meeting, the report said.

"I believe this is an expression of his willingness to eliminate all the unfortunate past and open a new future," Kim said of Trump, according to the AP. He added that he was "surprised" when Trump extended the invitation on Saturday.

Earlier, while taking in the view from Observation Post Ouellette at the DMZ before meeting with Kim, Trump told reporters that there has been "tremendous" improvement in U.S.-North Korea relations since the first summit with Kim in Singapore last June.