The decision follows the killing of three U.S. troops in a drone attack near the Jordan-Syria border - an attack that the Pentagon said bore the "footprints" of Kataib Hezbollah, though a final assessment had not yet been made.
Founded in the aftermath of the 2003 U.S.-led invasion of Iraq, Kataib Hezbollah is one of the elite Iraqi armed factions closest to Iran.
It is the most powerful armed faction in the Islamic Resistance in Iraq, an umbrella group of hardline Shi'ite armed groups that have claimed more than 150 attacks on U.S. forces since the Gaza war began in early October.
Iraq's government is backed by parties and militias close to Iran, though not directly by the hardline groups that have been firing on U.S. forces, Western and Iraqi officials say.
Baghdad has condemned the attacks while also saying regional escalation would continue as long as the Gaza war went on.
U.S. Defense Secretary Lloyd Austin vowed on Monday the U.S. would take "all necessary actions" to defend its troops after the deadly drone attack, even as President Joe Biden's administration stressed it was not seeking a war with Iran.
(Reporting by Timour Azhari; Editing by Chris Reese and Sandra Maler)
