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 Sunday.

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.

Fifteen fighters, including commanders, were killed in the U.S. strikes in western Iraq, an official from the Tehran-backed Hashed al-Shaabi paramilitary told AFP. The official said several fighters were also wounded in the strikes.

"In response to repeated Kata'ib Hizbollah attacks on Iraqi bases that host @CJTFOIR forces, U.S. forces conducted precision defensive strikes against 5 KH facilities in Iraq & Syria [to] degrade KH's ability to conduct future attacks against @coalition forces." ~@ChiefPentSpox pic.twitter.com/g2hmTD4Eqw

— OIR Spokesman Col. Myles B. Caggins III (@OIRSpox) December 29, 2019

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.

Later Sunday night, four rockets exploded near a base housing U.S. troops close to Iraq's capital, a security official said.

"Four Katyusha rockets exploded in the evening around the huge Taji Iraqi military base ... which houses American soldiers, without causing casualties," said the Iraqi official, who did not want to be named.

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 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.