The strikes come just hours after President Joe Biden and top defence leaders joined grieving families as the remains of the three Army Reserve soldiers were returned to the US.
The US military has launched an air assault on at least 85 targets in Iraq and Syria used by Iranian-backed militias on Friday.
Numerous aircraft were used – including long-range B-1 bombers flown from the US – marking the opening salvo of retaliation for the drone strike that killed three US troops in Jordan last weekend.
A statement from US Central Command said: “US Central Command (CENTCOM) forces conducted airstrikes in Iraq and Syria against Iran’s Islamic Revolutionary Guards Corps (IRGC) Quds Force and affiliated militia groups.
Middle East latest: US begins wave of airstrikes in Iraq and Syria
“US military forces struck more than 85 targets, with numerous aircraft to include long-range bombers flown from United States.
“The airstrikes employed more than 125 precision munitions.”
The strikes targeted “command and control operations, intelligence centers, rockets, and missiles, and unmanned aerial vehicle storages, and logistics and munition supply chain facilities”.
President Joe Biden and other top US leaders have been warning for days that the country would strike back at the militias, and made it clear that it would not be just one hit, but a “tiered response” over time.
Following the strikes, Mr Biden said in a statement: “Our response began today. It will continue at times and places of our choosing.
“The United States does not seek conflict in the Middle East or anywhere else in the world. But let all those who might seek to do us harm know this: If you harm an American, we will respond.”
Iraqi military spokesman Yahya Messenger Abdullah said: “The cities of Al-Qaim and the Iraqi border areas are being subjected to air strikes by United States aircraft, as these strikes come at a time when Iraq is striving to ensure the stability of the region.
“These strikes constitute a violation of Iraqi sovereignty, an undermining of the efforts of the Iraqi government, and a threat that will drag Iraq and the region into unforeseen consequences, the consequences of which will be disastrous for security and stability in Iraq and the region.”
The White House said it had informed Iraqi officials ahead of the military strikes.
An Iraqi security official told NBC News the US targeted a weapons warehouse and three houses belonging to Kata’ib Hezbollah in Anbar province, western Iraq.
Earlier on Friday, Mr Biden and top defence leaders joined grieving families as the remains of the three Army Reserve soldiers were returned to the US during a ceremony at Dover Air Force Base in Delaware.
The US strikes – of which there were three in Iraq and four in Syria – appeared to stop short of directly targeting Iran or its Revolutionary Guard Quds force.
Iran has denied it was behind the Jordan attack.
Before the retaliatory strikes, Iranian President Ebrahim Raisi said that Iran will not start a war but would “respond strongly” to anyone who tried to bully it.
Syrian State TV reported that “several” people had been killed and injured “as a result of the American aggression on a number of sites at the Badia and the Syrian-Iraqi border”.