WASHINGTON (AP) — The United States has asked Iraq for permission to put Patriot missile systems at bases hosting U.S. troops to improve defenses against attacks like the Jan. 8 Iranian missile strike that caused brain injuries to more than 50 U.S. troops, Pentagon officials said Thursday.

“That is one of the matters we have to work on and work through” with the Baghdad government, Defense Secretary Mark Esper told a Pentagon news conference. He and Army Gen. Mark Milley, chairman of the Joint Chiefs of Staff, made clear that they want Patriots in Iraq as part of an effort to improve protection of U.S. forces there.

The United States has about 5,000 troops in Iraq to train and advise Iraqi security forces in their fight against extremist groups like the Islamic State. The relationship is especially rocky in the aftermath of the American airstrike Jan. 3 that killed Qassem Suleimani, Iran's most powerful general, at Baghdad's international airport. The Iraqi government has indicated it could expel all foreign forces, although it has not yet taken action against the U.S. presence.

There were no Patriots or other air defenses in Iraq capable of shooting down ballistic missiles at the time of the Iranian strike that hit Ain al-Asad air base in western Iraq. Milley said the missiles were armed with 1,000-pound and 2,000-pound high-explosive warheads. He said it was fortunate that the attack caused no American loss of life or limb.

Milley said that in addition to securing Iraqi government permission, the U.S. military needs to work through mechanical and logistical issues to move a Patriot battalion to Iraq. There was not already one there because U.S. commanders judged that Iraq was a less-likely target for an Iranian ballistic missile attack than other Persian Gulf countries.

Asked whether the Iranian missiles could have been shot down before reaching their target if Patriots had been deployed at Ain al-Asad, Milley said, “That's what they're designed to do. Can't say for certain, obviously” that they would have succeeded.