Iraqi lawmakers have demanded US forces leave the country following a surprise visit by President Donald Trump that politicians denounced as arrogant and a violation of Iraqi sovereignty.

Politicians from both blocs of Iraq's divided parliament on Thursday called for a vote to expel US troops and promised to schedule an extraordinary session to debate the matter.

"Parliament must clearly and urgently express its view about the ongoing American violations of Iraqi sovereignty," said Salam al-Shimiri, a lawmaker loyal to the populist cleric Moqtada al-Sadr.

Trump, making his first presidential visit to troops in a troubled region on Wednesday, said he has no plans to withdraw the 5200 US forces in the country.

Containing foreign influence has become a hot-button issue in a year that saw al-Sadr supporters win the largest share of votes in May elections. Al-Sadr has called for curbing US and Iranian involvement in Iraqi affairs.

US troops are stationed in Iraq as part of the coalition against the Islamic State group. American forces withdrew in 2011 after invading in 2003 but returned in 2014 at the invitation of the Iraqi government to help fight the jihadist group.

But after defeating IS militants in their last urban bastions last year, Iraqi politicians and militia leaders are speaking out against the continued presence of US forces in Iraqi soil.

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 US forces from Iraq, or the militia and others would force them out by "other means".

Khazali was jailed by British and US forces from 2007 to 2010 for managing sections of the Shi'ite insurgency against the occupation during those years.

His militia is represented in parliament by the Binaa bloc, a rival coalition to al-Sadr's Islah. Binaa favours close ties with Iran and is aligned with Tehran on regional political issues.

Trump spent three hours at a US air base meeting with American troops during his visit. The president defended his decision to withdraw 2000 US forces from neighbouring Syria, saying the US military had all but eliminated IS-controlled territory there.

He left without meeting any Iraqi officials, though he spoke to Prime Minister Adel Abdul-Mahdi by phone.

The prime minister's office said in a statement after Trump's visit that "differences in points of view" over arrangements led to a face-to-face meeting between the two leaders to be scrapped.

Al-Shimiri said Trump's visit "violated several diplomatic norms".