(Adds visas processed in Baghdad; ordeal of family en route to NY)

* Plans to lobby Trump to mitigate impact of curbs on Iraqis

* Will argue that cooperation needed in war on Islamic State

* Former Iraqi translator for U.S. forces feels betrayed

* Under 500 special immigration visas in process for Iraqis

* Sadr, Shi'ite groups want Americans expelled from Iraq

By Maher Chmaytelli, Isabel Coles and Ahmed Rasheed

BAGHDAD/MOSUL, Iraq, Jan 29 (Reuters) - Iraq will lobby against new travel limits to the United States by Iraqis, arguing both countries need to uphold their fight against Islamic State (IS), Iraqi parliamentarians said on Sunday.

The Iraqi government has so far declined comment on an executive order signed by new U.S. President Donald Trump on Friday that suspends the entry of travelers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen for at least 90 days {nL1N1FH1XY].

The order stirred angry reactions in Iraq, where more than 5,000 U.S. troops are deployed to help Iraqi and regional Kurdish forces in the war against IS insurgents.

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

"Iraq is in the front line of the war on terrorism ... and it is unfair that the Iraqis are treated in this way," parliament's foreign affairs committee said in a statement.

"We call on the Iraqi government to retaliate for the decision taken by the U.S. administration," it added after a session on Sunday in Baghdad.

Baghdad plans to lobby Washington to review the decision, according to two lawmakers who declined to be identified.

One of them told Reuters that the government will "explain that Iraq as a sovereign country will be forced to apply similar treatment, and that would affect negatively cooperation, including military cooperation", in the conflict with IS.

Popular Mobilization, a coalition of mainly Shi'ite Muslim paramilitary groups armed and trained by Iran to fight Islamic State, urged Prime Minister Haider al-Abadi's government to expel U.S. nationals.

Influential Shi'ite cleric Moqtada al-Sadr said on Sunday American citizens should leave Iraq. "It would be arrogance for you (Americans) to enter Iraq and other countries freely while barring them entrance to your country ... and therefore you should get your nationals out," he said on his website.

CRITICAL U.S. SUPPORT AGAINST ISLAMIC STATE

The U.S.-led coalition is providing critical air and ground support to Iraqi forces 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.