WASHINGTON, Dec. 29 (Xinhua) -- The Pentagon said on Sunday the U.S. military had carried out strikes against Iran-backed military group in Iraq and Syria, two days after a rocket attack on an Iraqi base leading to the death of a U.S. civilian contractor.

U.S. forces have conducted "precision defensive strikes" against three Kata'ib Hezbollah (KH) facilities in Iraq and two in Syria, Assistant to the Secretary of Defense Jonathan Hoffman said in a statement.

According to local media, at least 25 militia fighters were killed and at least 55 wounded following U.S. strikes in Iraq.

The Pentagon pointed out that the military raid was a response to the KH rockets attack on an Iraqi base near Kirkuk on Friday, which killed a U.S. civilian contractor and injured four U.S. service members and two members of the Iraqi Security Forces (ISF).

KH has a strong linkage with Iran's Quds Force and has repeatedly received lethal aid and other support from Iran, according to the statement.

Calling the attack "successfull," U.S. Defense Secretary Mark Esper told reporters that U.S. President Donald Trump was informed that further military responses could be warranted.

"We discussed with him other options that are available," said Esper. "I would note also that we will take additional actions as necessary to ensure that we act in our own self-defense, and we deter further bad behavior from militia groups or from Iran."

More than 5,000 U.S. troops have been deployed in Iraq to support the Iraqi forces in the battles against Islamic State (IS) militants, mainly providing training and advising to the Iraqi forces.

The troops are part of the U.S.-led international coalition that has been conducting air raids against IS targets in both Iraq and Syria.