Iraq is so far the only one of the seven targeted countries to propose a reciprocal measure.
President Donald Trump's inclusion of Iraq in the temporary ban on foreign nationals entering the US has alarmed American diplomats who warn it risks upending delicate military, political and business ties at a time when Islamic State is on the cusp of defeat in the country.
World leaders including Canadian Prime Minister Justin Trudeau and German Chancellor Angela Merkel have denounced the USA ban, which also targets citizens of Iran, Libya, Somalia, Sudan, Syria and Yemen - including those with dual citizenship.
Some members of parliament said Iraq should retaliate with similar measures against the United States.
The move has sparked anger in Iraq, whose forces have been fighting against the Islamic State group with American assistance for more than two years, and led to calls for a reciprocal ban on U.S. citizens.
Iraqi lawmakers on Sunday called for their government to ban US citizens from going into Iraq.
"Parliament voted by majority on calling on the Iraqi government and the foreign ministry to respond in kind", MP Hakim al-Zamili said.
Lawmaker Sadiq Al says 'we hope that the American administration will rethink this decision.
Hassan Shwairid, the deputy head of the committee, said that the call did not apply to the thousands of American military personnel in the country as part of the US-led coalition against Daesh.But US Senators John McCain and Lindsay Graham said Trump's ban would impact military cooperation and security in other ways.
A foreign ministry official said that meetings were ongoing to determine Iraq's response.
Trump's decision led to the detention of incoming refugees at U.S. airports, sparking protests, legal challenges and widespread condemnation from global leaders, rights groups and activists.
The most powerful groups in the Hashed al-Shaabi are Iran-backed Shiite militias, some of whom fought against United States forces in previous years.
Trump's travel restrictions drew condemnation from influential Shia leader Muqtada al-Sadr.
"It would be arrogance for you to enter freely Iraq and other countries while barring to them the entrance to your country. and therefore you should get your nationals out, " Moqtada al-Sadr said on his website.