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.
