David Schenker, the assistant secretary of state for Middle East policy under Mr. Trump, said it was the responsibility of Iraq’s Shiite-led government to constrain the militias that were backed by Iran.
“I don’t think that by showering blandishments on Iran that you’re going to get better behavior in Iraq,” Mr. Schenker, now a senior fellow at the Washington Institute for Near East Policy, said in an interview. “Ultimately, this is all about Iran — the missiles, the weaponry, the funding, the direction all comes from Tehran.”
Military officials say that 14 107-millimeter rockets were launched in the Erbil attack, but six misfired. The attack from territory controlled by Kurdish forces has raised concerns about security gaps in what has been considered the safest region of Iraq.
A little-known group known as Awliya al Dam, or Guardians of the Blood, brigades claimed responsibility for the attack, but it offered no evidence. The group claimed responsibility last August for two bombings targeting U.S. contractor convoys carrying military equipment.
An antirocket system was in place and operating at the Erbil airport at the time of the attack, but the rockets landed in an area not covered by the system, an American military official said.
U.S. commanders have said that the 2,500 troops now in Iraq — about half the number from last summer — would be sufficient not only to act as a bulwark against Iranian proxies and other influences, but also to help Iraqi security forces hunt down remaining pockets of Islamic State fighters.