Moon, who backs engagement with nuclear-armed North Korea, was to meet Thursday with Trump during his first foreign outing since being sworn in last month after a landslide election win.
Late last week, he was scheduled to take part in a wreath-laying ceremony at a war memorial in Quantico, Virginia, and later was to attend summit of Korean and American business leaders.
His agenda today includes meetings with lawmakers on Capitol Hill and an evening visit with the US president and First Lady Melania Trump, including a reception and dinner.
Pyongyang is seeking to develop nuclear-capable ballistic missiles that could reach the continental United States.
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Trump has been pushing for tougher sanctions against Pyongyang to curb its nuclear ambitions and whose administration has said military action was a possibility.
Also expected to be high on the agenda is likely to be a controversial US missile defense system that has been installed in South Korea to guard against missile threats from the North.
Officially, the delay is to allow for a new, comprehensive environmental impact assessment, but analysts say the move is a strategic one by Moon to delay the tricky diplomatic situation he inherited.