"We have been given assurances that the [US] support will not only continue but will accelerate for Iraq to accomplish the task", he said after his first meeting with the USA president.
Iraq's Prime Minister Haider al-Abadi met with Donald Trump on 20 March at the White House and the two leaders discussed accelerating efforts to put an end to the Islamic State.
AP also reported Trump as having said the U.S "shouldn't have gone in" to Iraq in the first place.
Recognizing that terrorism can not be defeated by military might alone, Trump and al-Abadi also agreed to promote an extensive political and economic partnership between the two countries.
The Iraqi premier's first visit to Washington since Trump's inauguration came before Trump hosts a 68-nation meeting geared toward advancing the fight against the militant group.
He said: "I can sense a difference in terms of being head-to-head with terrorism".
Al Abadi said he hasn't seen Trump's plan to defeat ISIS, but praised his tough rhetoric against the Islamic extremists.
He added: "We will figure something out".
Trump said he also would address what he described as a "vacuum" that was created when so-called Islamic State (IS) militants took over large swaths of territory in western and northern Iraq.
"Certainly, we shouldn't have left".
Before leaving the Iraqi capital Baghdad for the afternoon meeting, Abadi said in a video statement, "We are in the last chapter, the final stages to eliminate ISIL militarily in Iraq". "I think we are happy with the [White House] meeting. and we're looking forward to meeting with Congress and others", he said.
Trump said his main thrust is to get rid of the ISIS. But al-Abadi grabbed Trump's arm and joked, "we had nothing to do with the wiretap". "It will happen. It's happening right now", he said. At the forum, Abadi called for more financial contributions from the global community. "We shouldn't be derailing the whole thing" or losing focus against ISIS because of clashes among the region's major actors", he said.
The Iraqi premier also thanked the United States president for removing Iraq from a travel ban affecting several Muslim-majority countries.
The Iraqi prime minister was less enthusiastic about the global humanitarian community's follow-through on pledges made to support his country, where 3 million are internally displaced and 11 million people need humanitarian assistance.