Last month, the two leaders discussed the battle against Islamic State during a phone call, but on Monday they will have their first face-to-face meeting.
Before departing for Washington, Abadi said he wanted to talk with Trump about 'how to complete the final stages to defeat ISIS and those who are helping them.'
Iraqi forces have been battling the militants on the ground with the help of air support from a U.S.-led coalition that has been targeting Islamic State since August 2014.
Battle for Mosul
The battle to regain control of Mosul began late last year and has so far resulted in Iraqi troops capturing the eastern part of the city and making gains in the western portion.
Iraqi helicopters on Sunday fired rockets near a key mosque in western Mosul as ground forces closed in on the site where Islamic State leader Abu Bakr al-Baghdadi declared a self-styled caliphate in 2014.
U.S. and Iraqi analysts have eyed the mosque as the jihadists' unofficial administrative headquarters.
At one point late Sunday, witnesses reported Iraqi ground forces within 100 meters of Mosul's wrecked Iron Bridge, pressing slowly toward the nearby mosque in an offensive slowed by narrow roadways and the presence of hundreds of thousands of civilians.
'The difficulties are the presence of families, how to avoid opening fire on families who are used as human shields' by the jihadists, said General Abbas al-Juburi in comments to the French news agency.
Juburi also linked the slow pace of the days-old offensive to the lack of artillery in the ancient neighborhoods of the Old City, where buildings are too close together and roadways too narrow to support the use of such weaponry.
More ethnic Yazidis freed
In other developments, the Kurdish news agency Rudaw said eight more captive ethnic Yazidi women and children were rescued Sunday from their IS captors.
Details were sketchy. But the report quoted Kurdish rescue official Hussein Koro as saying the operation was coordinated with Kurdish peshmerga fighters and security agencies north of Mosul in Duhok province.
Koro said 2,000 Yazidis have been rescued since Islamic State seized much of Kurdish northern Iraq three years ago. But he said 3,400 others remain captive.
Islamic State kidnapped thousands of Yazidi women and children in August 2014 when it attacked their homes and villages in northwestern Iraq near the Syrian border. Iraqi Kurdish forces backed by U.S. airstrikes have since recaptured some of that territory, but many children have been orphaned and many young women are believed to have been taken into slavery.
Escapees say the slaves are often victims of rape and subjected to forced labor.
Runaways also have reported that slaves are closely tracked and that many of them are recaptured, only to face more punishment.