The disaster took place hours after Iran launched its missile attack on USA forces.
Iran, which has long said United States forces should leave the Middle East, told Washington after the attacks to withdraw its troops to prevent more deaths and warned U.S. allies including Israel not to allow attacks from their territories.
Syria is Iran's most reliable ally in the region.
Also read: Who is Qasem Soleimani of Iran?
Additionally, "U.S. forces and air-defense missile batteries across the Middle East were placed on high alert overnight Monday to possibly shoot down Iranian drones as intelligence mounted about a threat of an imminent attack against U.S. targets", reported CNN, citing two U.S. officials.
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The official said five members of the militia were killed in the latest strike. The head of the Revolutionary Guard's foreign wing, or Quds Force, Gen.
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Global powers had warned Friday that the killing of Soleimani could spark a risky new escalation, with many calling for restraint. Netanyahu cut short his visit to Greece amid concerns Iran could exact revenge on the Jewish state for the USA strike.
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A source in the Kurdistan Regional Government (KRG) confirmed to ABC News that three missiles were fired at the global airport and adjoining U.S. military base. The bases are Irbil and Al-Asad.
Following the news of the attack, Iranian chief negotiator and chief leader Saeed Jalili reflected President Trump's response to the US airstrike in which senior military leader Qasem Soleimani was killed last week.
The White House said it is aware of the reports.
Mr Trump said, if we leave that would mean that Iran would have a much bigger foothold and the people in Iraq do not want to see Iran running the country. Iran's Islamic Revolutionary Guard Corps described the move through their Press TV as their revenge for the killing of top Iranian General Qassem Soleimani.
"I think we should expect that they will retaliate in some way, shape or form", he told a briefing at the Pentagon.
The foreign minister denied that Iran has control over such groups, and said whatever retaliation they might seek would be separate and apart from Tehran's own.