BAGHDAD, March 3 (Reuters) — Ten rockets landed on Wednesday at Iraq's Ain al-Asad air base, which hosts U.S., coalition and Iraqi forces, the Iraqi military said.

There were no reports of injuries among U.S. service personnel but an American civilian contractor died after suffering a "cardiac episode" while sheltering from the rockets, Pentagon spokesman John Kirby said in a statement.

"We cannot attribute responsibility at this time, and we do not have a complete picture of the extent of the damage," Kirby added. No group immediately claimed responsibility for the attack.

The United States is assessing the impact of the attack and whoever was responsible, White House spokeswoman Jen Psaki said.

"If we assess that further response is warranted, we will take action again in a manner and time of our choosing," she told a news briefing. "What we won't do is make a hasty or ill-informed decision that further escalates the decision or plays into the hands of our adversaries."

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Last Thursday, U.S. forces carried out air strikes against facilities at a border control point in Syria used by Iranian-backed militias including Kata'ib Hezbollah and Kata'ib Sayyid al-Shuhada.

A Baghdad Operations Command official said Wednesday's attack was launched from a location about eight km (five miles) from the base, which is in the westerly Anbar province.

Another Iraqi security source and a government official who spoke on condition of anonymity said the rockets had been launched from a point west of the nearby town of Baghdadi.

Despite a deterioration in security in some parts of the country, Pope Francis is due to begin a four-day visit to Iraq on Friday.

On Feb. 16, a rocket attack on U.S.-led forces in northern Iraq killed a civilian contractor and injured a U.S. service member.