The United States is not seeking to escalate its simmering conflict with Iran, a senior official said Monday after the Pentagon launched air strikes on Tehran-allied Iraqi militia forces.

US Assistant Secretary of State David Schenker said the Sunday strikes on Hezbollah Brigades bases were a message to Iran after months of "restraint" by the administration of President Donald Trump.

Schenker said the strikes, which reportedly killed 25, were to retaliate for the death Friday of a US civilian contractor in Kirkuk in a Hezbollah Brigades rocket attack.

"We thought it important to hit a significant target set to send a very clear message to them about how serious we take American lives," Schenker told reporters.

"This was a response that was serious, but was, I think in many ways, proportionate," he said.

"We don't want an escalation here, we want a de-escalation."

Brian Hook, the State Department's Special Representative for Iran, said Washington had held back from responding despite a series of attacks tied to Iran, including 11 rocket assaults on US and coalition installations in Iraq since October.

"The president has been very patient. He has shown a great deal of restraint," Hook said.

"We very much hoped that Iran would not miscalculate and confuse our restraint for weakness. But after so many attacks, it was important for the president to direct our armed forces to respond in a way that the Iranian regime will understand."

"We will not tolerate attacks against US citizens, our military or our partners and allies in the region," Hook added.

On Sunday night, US planes hit several bases in Iraq and Syria belonging to the Hezbollah Brigades, one of the most radical factions in the Hashed al-Shaabi, an Iraqi paramilitary coalition.

The strikes "killed 25 and wounded 51, including commanders and fighters, and the toll could yet rise," according to the Hashed, which has significant influence in Iraq.