"The operation is underway" and is targeting weapons facilities, one official said on condition of anonymity, without specifying where the strikes were taking place.

"US air strikes targeted Hashed al-Shaabi positions in multiple provinces across Iraq, targeting logistics nodes and UAV (drone) storage units," said a second official, adding that the Iran-backed armed faction Kataeb Hezbollah was one of those targeted.

Earlier Thursday US Defense Secretary Mark Esper warned that "all options are on the table" to respond to the death of the three soldiers in a rocket attack on the Taji air base on Wednesday.

Fourteen others were injured in the attack, including Americans, British, and Poles.

The rocket attack sparked fears of a fresh escalation of tensions between the United States and Iran.

While there was no immediate claim of responsibility for the attack, which saw about 18 rockets land on the base, Washington has blamed Iran-backed factions from the Hashed al-Shaabi military network for recent similar violence.

"The strikes began at 1:00 am local time and are using various kinds of aircraft," one of the sources said.

"We have no immediate information on casualties," the official added.

"This is the response to the rocket attacks yesterday.... This is not a coalition operation. This a specifically US operation."