Iraq has said a revised US travel ban which removes the country from a list of Muslim-majority nations sends a "positive message" about the future of bilateral relations as the two countries work to combat Islamic State (IS).

Government spokesman Saad al-Hadithi said the decision to revise the ban shows that there is a "real partnership" between Washington and Baghdad.

An earlier version of the travel ban, which was signed in January before being suspended by the courts, banned Iraqis and the citizens of six other countries from entering the United States.

The move sparked anger among many Iraqis, and prompted Iraqi MPs to call for a reciprocal order banning Americans from Iraq.

Iraq was among seven Muslim-majority countries whose nationals were temporarily banned from travelling to the United States in an earlier order issued by President Trump in January, which was blocked by the courts.

The White House had said the earlier ban was needed to prevent terrorists from entering the country, but has now removed Iraq from the list under pressure from the state department and the defence department, which had noted the close cooperation between the two countries in battling IS militants in the northern Iraqi city of Mosul.

The revised order is narrower and specifies that a 90-day ban on people from Sudan, Syria, Iran, Libya, Somalia and Yemen does not apply to those who already have valid visas.

Thousands of American forces are in Iraq providing air support and logistical help for a massive operation to drive IS militants from Mosul, the country's second largest city.

Smaller numbers of US special operations forces are embedded with some Iraqi units.

Support from a US-led coalition has been critical in the fight against IS, helping Iraqi forces to slowly roll back the militants over the past two and a half years.

Iraqi forces are now in the midst of their toughest battle yet against IS as they push to retake Mosul's west after the eastern half of the city was declared "full liberated" in January.

Iraqi troops on the front lines welcomed the revision to the travel ban while still expressing anger over the original order.

"To be honest, (the original ban) made me upset and that will not change," said Sgt Maj Asad al-Asadi of Iraq's special forces, who has been away from home battling the IS group for nearly three years.

"I've lost three friends fighting terrorists and Trump calls me a terrorist."