Iraq plans to lobby against new restrictions on travel to the United States by Iraqis, arguing the two countries need to preserve their alliance against Islamic State, two members of the Iraqi parliament, who declined to be identified, said on Sunday.

The Iraqi government itself has so far declined to comment on an executive order signed by U.S. President Donald Trump on Friday, which suspends the entry of travelers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen for at least 90 days.

The order caused angry reactions in Iraq, where more than 5,000 U.S. troops are deployed, helping Iraqi and Kurdish forces in the war on Islamic State.

Some members of the parliament said Iraq should retaliate with similar measures against the United States.

"Iraq is in the frontline of the war on terrorism (...) and it is unfair that the Iraqis are treated in this way," said the parliament's foreign affairs committee.

"We ask the Iraqi government to reciprocate to the decision taken by the U.S administration," the committee said in a statement after a meeting on Sunday in Baghdad.

Popular Mobilization, a coalition of mainly Shi'ite paramilitary groups armed and trained by Iran to fight Islamic State, called on the Iraqi government to expel U.S. nationals.

"The foreign ministry will be contacting the U.S. administration to review their decision,'' said an MP who sits on the parliament's foreign relations committee.

The Iraqi government will "explain that Iraq as a sovereign country will be forced to reciprocate, and that would affect negatively cooperation, including military cooperation in the war" on Islamic State, a second lawmaker said.

The U.S.-led coalition is critical in the ongoing battle to wrest Mosul, the largest city in northern Iraq, from Islamic State.

Mosul is the last major Iraqi city still under the control of Islamic State, the ultra-hardline Sunni group that declared a self-styled "caliphate" over parts of Iraq and Syria in 2014.

The government announced on Tuesday that Iraqi forces have taken over the part of Mosul on the eastern bank of the Tigris River, which divides the city, and were preparing to attack the militants on the western bank.