The premier's office said Abadi would also meet Vice President Mike Pence and Secretary of State Rex Tillerson, without giving specific dates.
On Wednesday, the prime minister is to take part in a ministerial meeting of the 68-nation coalition lined up against the Islamic State group.
Iraqi authorities in October launched an offensive to retake the northern city of Mosul from IS with the support of US-led coalition air strikes.
The Iraqi government earlier this month welcomed its nationals' exemption from a revised travel ban drawn up by Trump as an "important step" that strengthens ties between Baghdad and Washington.
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