BAGHDAD — An Iraqi militia official on Saturday hinted at a desire to de-escalate tensions in the Middle East following retaliatory strikes launched by America against dozens of sites in Iraq and Syria used by Iranian-backed militias and the Iranian Revolutionary Guard.

A spokesman for Harakat al-Nujaba, one of the main Iranian-backed militias in Iraq, in an interview with the Associated Press at Baghdad condemned the strikes, saying Washington “must understand that every action elicits a reaction.”

The spokesman, Hussein al-Mosawi, then struck a more conciliatory tone, saying that “we do not wish to escalate or widen regional tensions.”

Mr. Mossawi said the targeted sites in Iraq were mainly “devoid of fighters and military personnel at the time of the attack.” Suggesting there was not too much damage could allow him to justify the lack of a strong response.

Syrian state media reported that there were casualties from the strikes but did not give a number. The head of the Britain-based Syrian Observatory for Human Rights, Rami Abdurrahman, said that 23 people were killed in the Syria strikes, all rank-and-file fighters.

An Iraqi government spokesman, Bassim al-Awadi, said in a statement Saturday that the strikes in Iraq near the Syrian border killed 16, including civilians, and there was “significant damage” to homes and private properties.

An American official said Saturday that an initial battle damage assessment showed America had struck each of its planned targets in addition to a few “dynamic targets” that popped up as the mission unfolded, including a surface to air missile site and drone launch sites. 

The official, who spoke on the condition of anonymity to provide details that were not yet public, did not yet have a casualty assessment.

Iraq’s foreign ministry announced Saturday it would summon the American embassy’s chargé d’affaires — the ambassador being outside of the country — to deliver a formal protest over American strikes on “Iraqi military and civilian sites.”

The air assault was the opening salvo of American retaliation for a drone strike that killed three service members in Jordan last weekend. America has blamed that on the Islamic Resistance in Iraq, a coalition of Iranian-backed militias.

Iran, meanwhile, has attempted to distance itself from the attack, saying that the militias act independently of its direction.

The Iraqi spokesman, Mr. al-Awadi, condemned the strikes as a violation of Iraqi sovereignty, particularly since some of them targeted facilities of the Population Mobilization Forces. 

The group, a coalition of Iranian-backed militias, was officially brought under the umbrella of the Iraqi armed forces after it joined the fight against the Islamic State in 2014, but in practice it continues to operate largely outside of state control.

The Popular Mobilization Forces said in a statement Saturday that one of the sites targeted was an official security headquarters of the group. In addition to 16 killed, it said 36 had been wounded, “while the search is still ongoing for the bodies of a number of the missing.”

The Iraqi government has been in a delicate position since a group of Iranian-backed Iraqi militias calling itself Islamic Resistance in Iraq — many of whose members are also part of the PMF — began launching attacks on American bases in Iraq and Syria on October 18. The group described the strikes as retaliation for Washington’s support for Israel in the war in Gaza.

Iraqi officials have attempted behind the scenes to rein the militias in, while also condemning American retaliatory strikes as a violation of the country’s sovereignty and calling for an exit of the 2,500 American troops in the country as part of an international coalition to fight the Islamic State. 

Last month, Iraqi and American military officials launched formal talks to wind down the coalition’s presence, a process that will likely take years.

One of the main Iran-backed militias, Kataib Hezbollah, said it was suspending attacks on American troops following Sunday’s strike that killed the American troops in Jordan, to avoid “embarrassing” the Iraqi government.

Meanwhile Saturday, the Central Command acknowledged it had had a series of skirmishes in the Red Sea and the Gulf of Aden with Yemen’s Houthi rebels. 

On Friday, the United States Ship Carney shot down a drone over the Gulf of Aden and there were no injuries or damage. America also conducted airstrikes on four Houthi drones preparing to launch that it said “presented an imminent threat to merchant vessels and the U.S. Navy ships in the region.”

Overnight, F/A-18 fighter jets from the United States Ship Dwight D. Eisenhower aircraft carrier shot down seven drones in the Red Sea along with the United States Ship Laboon.