Top American military officials including Gen. Mark Milley, chairman of the Joint Chiefs of Staff, and Defense Secretary Mark Esper have also said there were no plans for the United States to withdraw from Iraq.
Pompeo said Washington would continue its mission to help train Iraqi security forces and counter the Islamic State group.
At least four Iraqi soldiers have been injured in mortar shelling targeting Al-Balad airbase housing American troops.
More than 5,000 U.S. troops have been deployed in Iraq to support the Iraqi forces in the battles against Islamic State militants.
The Wall Street Journal reported Saturday that the State Department threatened to cut off Iraq's New York Fed account in a phone call Wednesday with Prime Minister Adel Abdul-Mahdi, according to unnamed Iraqi officials.
"There are American forces entering Iraq and American drones flying in its sky without permission from the Iraqi government", Abdul Mahdi noted.
There are roughly 50,000 American troops in the Middle East - with several thousand more on the way - 6,000 of whom are in Iraq.
However, the State Department said in a statement on Friday that Washington would not hold discussions with Baghdad regarding USA troop withdrawal. "And now those same protesters are turning against us, including the Iraqi parliament".
Still, the demand for withdrawal is not universal.
The latest escalation was set off when a rocket attack blamed on the Iranian-backed militia group Kataeb Hezbollah caused the death of a United States contractor at a base in Kirkuk province.
How do Iraqi citizens feel about the USA military presence in their country? That coalition stood down from its campaign against the terrorist group after Soleimani's killing to concentrate on defending USA bases.
Abdul-Mahdi resigned past year but has continued to preside over the government in an acting capacity.
"The Iraqi government must work to end the presence of any foreign troops on Iraqi soil and prohibit them from using its land, airspace, or water for any reason", the nonbinding resolution said, according to Reuters.
The adviser said both Iraq and the U.S. were warned of the impending attack by one Arab country and one European country, declining the name them.
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