Iraqi lawmaker, Hakim al-Zamili, speaks to the media during press conference, in Baghdad, April 18, 2016.
Iraqi MPs told Reuters news agency that Mr Trump had asked for the meeting to take place at the al-Asad military base, an offer declined by the prime minister.
"They should be sharing the burden of costs and they're not", the US President said.
"There was supposed to be a formal reception and a meeting between Prime Minister Adil Abdul-Mahdi and the US President, but a variation of views to organize the meeting led it to be replaced by a telephone conversation on developments in the situation", the statement read.
Qais Khazali, the head of the Iran-backed Asaib Ahl al-Haq militia, promised on Twitter that Iraq's parliament would vote to expel U.S. forces from Iraq, or the militia and others would force them out by "other means".
Qais Khazali, the head of the Iran-backed Asaib Ahl al-Haq militia that fought key battles against IS in north Iraq, promised on Twitter that Parliament would vote to expel USA forces from Iraq, or the militias would force them out by "other means".
Trump said he has "no plans at all" to order a withdrawal of American forces from Iraq, similar to what he ordered for USA troops in Syria last week.
Trump has argued that the U.S. now no longer needs to be present in Syria as the ISIS terror group has been defeated.
"We don't want to be taken advantage of any more by countries that use us and use our incredible military to protect them". We are spread out all over the world. "Frankly, it's ridiculous", he added.
Iraq and the USA have reduced the territory held by ISIS to nearly nothing, but sporadic violence continues and there remains the possibility ISIS members will melt into an insurgency. "It's time to get our soldiers out, and it's time to get our young people out", Trump said, sitting next to military leaders and advisors.
"You're modern day warriors", Trump said, praising the troops.
Trump also said he had no plans to withdraw the 5,200 USA forces in Iraq. Trump sought to highlight the achievements of the four year war on ISIS, including what he said was the liberation of 20,000 square miles of territory and 3 million civilians.
Trump's visit to Iraq did not clarify his administration's position in the Middle East so much as underscore his apparently competing desires to both withdraw from the world and to project military power and strength.
Pundits back in the U.S. cried foul, denouncing the video as a violation of operational security for revealing the presence of SEAL Team Five in Iraq.
Al-Shimiri said Trump's visit "violated several diplomatic norms".
Still, after defeating IS militants in their last urban bastions a year ago, Iraqi politicians and militia leaders are speaking out against the continued presence of USA forces on Iraqi soil.
His militia is represented in parliament by the Binaa bloc, a rival coalition to al-Sadr's Islah. Sadr has long opposed the American presence in Iraq since the US-led invasion toppled Saddam Hussein in 2003. He led two uprisings against United States forces in Iraq and is one of the few Shia leaders to also distance himself from Iran.
Certainly, the Iraq that Trump is visiting is in a very different neighborhood than the one that Obama visited in 2009.
"If you would have seen what we had to go through in the darkened plane with all windows closed with no light anywhere - pitch black", he said.
The Iraq trip provided some distraction from a rising tide of domestic political problems, including a government shutdown caused by Trump's row with the US Congress over funding for a US-Mexico border wall.