Baghdad called Monday for the United States to review its "wrong decision" to prevent Iraqis from entering the country as parliament backed reciprocal restrictions if Washington does not change course.

The responses from Baghdad are part of a growing backlash against President Donald Trump's executive order barring citizens of Iraq, Iran, Syria, Sudan, Somalia, Libya and Yemen from entering the US for at least 90 days, a decision he billed as an effort to make America safe from "radical Islamic terrorists".

The travel restrictions, which come on the heels of repeated assertions by Trump that the US should have stolen Iraq's oil before leaving in 2011, risk alienating the citizens and government of a country fighting against militants the president has cast as a major threat to America.

"We reject... the decision to prevent the reception of Iraqis in the United States of America, and call for its review," Foreign Minister Ibrahim al-Jaafari told US ambassador Douglas Silliman, according to a statement on his website.

But "we (also) confirm our commitment to establishing better relations between Baghdad and Washington," Jaafari said.

The foreign ministry also issued a statement calling on the US to "review this wrong decision".

"It is very unfortunate that this decision was issued towards an allied state linked by strategic partnership with the United States," it said.

The ministry noted the US move "coincides with victories achieved by (Iraq's) brave fighters and with the support of the international coalition against the Daesh terrorist gangs in Mosul," referring to the battle to retake the city from the Islamic State jihadist group.

Parliament, meanwhile, urged the government to take similar measures against Americans if Washington does not reconsider its position.

Lawmakers voted for "a policy of reciprocity with the American decision in the event that the American side does not withdraw its decision," according to text read out before the vote.

It also called for the US Congress to pressure the Trump administration to reconsider its decision, and for the UN, Arab League and the Organisation of Islamic Cooperation to oppose the measure.

- Security ramifications -

And it said that if the US does not roll back the move, this "will push Iraq to take policies and decisions commensurate with the preservation of its interests."

"We are against this stance from the new administration," lawmaker Sadiq al-Laban told AFP.

"We hope that the American administration will rethink... this decision," he added.

Trump's decision led to the detention of incoming refugees at US airports, sparking protests, legal challenges and widespread condemnation from rights groups.

The parliamentary vote came a day after its foreign affairs committee made a similar call for Iraq to respond in kind to the US measure.

Hassan Shwairid, the deputy head of the committee, said the committee's call did not apply to the thousands of American military personnel in the country as part of the US-led coalition against IS.

The Pentagon on Thursday pledged to lobby for US entry of Iraqis who have worked for the US military, including fighters and translators.

And US senators John McCain and Lindsay Graham said Trump's ban could impact military cooperation and security in other ways.

"This executive order bans Iraqi pilots from coming to military bases in Arizona," where they have received training, they said in a joint statement.

"Ultimately, we fear this executive order will become a self-inflicted wound in the fight against terrorism."

Iraq's former ambassador to Washington Lukman Faily told AFP the ban was a "betrayal" as Iraq is a partner with the United States, fighting against militants.

The Hashed al-Shaabi, a powerful paramilitary umbrella organisation that includes Iran-backed Shiite militias that fought against American forces in past years, appealed Sunday for US citizens to be banned from the country.

Units from the Hashed and American troops are both deployed in the Mosul area as part of the operation to retake the city from IS, and heightened anti-US sentiment among militiamen could increase the danger to Washington's forces.

Trump's travel restrictions also drew condemnation from populist Shiite cleric Moqtada al-Sadr, America's bete noir for much of its 2003-2011 war in Iraq.

"Get your nationals out before removing expatriates," said Sadr, scion of a powerful clerical family who rose to widespread fame due to his condemnation of and violent resistance to the US invasion and occupation of Iraq.