WASHINGTON >> The U.S. carried out military strikes in Iraq and Syria targeting a militia blamed for an attack that killed an American contractor, a Defense Department spokesman said today.

U.S. forces conducted “precision defensive strikes” against five sites of Kataeb Hezbollah, or Hezbollah Brigades, an Iran-backed Iraqi militia, spokesman Jonathan Hoffman said in a statement.

The U.S. blames the militia for a rocket barrage Friday that killed a U.S. defense contractor at a military compound near Kirkuk, in northern Iraq.

Officials said attackers fired as many as 30 rockets in Friday’s assault.

The Defense Department gave no details immediately on how the strikes were conducted. It said the U.S. hit three of the militia’s sites in Iraq and two in Syria, including weapon caches and the militia’s command and control bases.

Hoffman said the U.S. strikes will weaken the group’s ability to carry out future attacks on Americans and their Iraqi government allies.

Iraq’s Hezbollah Brigades, a separate force from the Lebanese group Hezbollah, operate under the umbrella of the state-sanctioned militias known collectively as the Popular Mobilization Forces. Many of them are supported by Iran.

A senior member of the Popular Mobilization Forces, who spoke on condition of anonymity because he was not authorized to speak to the news media, said at at least 12 fighters with the Hezbollah Brigades had died in U.S. strikes along the Iraq and Syria border. His account could not immediately be independently confirmed.