The U.S government announced on Friday that the US consulate in the southern Iraqi city of Basra is being temporarily closed amid violence, including a rocket aimed at the consulate, by the Iranian-backed militias.
Some militia leaders in Basra accused protesters of colluding with the USA, which has long worked to curb Iranian influence in Iraq.
Basra hosts one of three US diplomatic missions in Iraq.
"We look to all worldwide parties interested in peace and stability in Iraq and the region to reinforce our message to Iran regarding the unacceptability of their behaviour".
"The ministry regrets the American decision to pull its staff out of Basra", Iraq's foreign minsitry said in a statement on Saturday.
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Hours before Pompeo's decision to close the consulate, rockets or mortars landed near the building, an official said.
Iran has condemned as irrational and unjustifiable the remarks made by the U-S secretary of state over the closure of the country's consulate in the Iraqi city of Basra.
In a speech addressing the United Nation's General Assembly speech earlier this week, President Trump hammered Iran over its support for terrorism and aggression against USA allies in the Middle East.
National security adviser John Bolton's issued a stark warning to Iran at the United Nations General Assembly on Tuesday, "If you cross us, our allies, or our partners; if you harm our citizens; if you continue to lie, cheat, and deceive, yes, there will indeed be hell to pay".
An Iraqi protester holds up an Iranian flag as another sets it on fire, next to a portrait depicting Iran's former and current Supreme Leaders Ayatollah Khomeini and Khamenei, during demonstrations against the government and the lack of basic services in Basra on September 7, 2018. Neighbouring Iran is the other major outside power present in Iraq, alongside bitter foe the United States which led the 2003 invasion that toppled veteran dictator Saddam Hussein.
But those tensions have eased in recent weeks as Iraqi politicians bore down on accelerating the government formation process amid the pressure from Basra's protest movement.