The second such deadly raid on pro-Iran targets since US President Joe Biden took office, described by the Pentagon as "retaliatory", has sparked fears of a new US-Iran escalation amid faltering efforts to revive a multilateral deal over Tehran's nuclear programme.

"This action in self-defence... sends a very important and strong message," Blinken told reporters on a visit to Rome.

"I would hope that the message sent by the strikes last night will be heard and deter future action," he added, referring to repeated attacks against US interests in Iraq that Washington blames on pro-Iran groups.

But Iraq's Prime Minister Mustafa al-Kadhemi condemned the US strikes as a "blatant and unacceptable violation of Iraqi sovereignty and Iraqi national security".

"Iraq reiterates its refusal to be an arena for settling scores," Kadhemi added in a statement, urging all sides to avoid any further escalation.

The Hashed-al-Shaabi, an Iraqi paramilitary alliance that includes several Iranian proxies and has become the main power broker in Baghdad, said the strikes killed four of its fighters in the Qaim region, near the border with Syria.

The fighters were stationed there to prevent jihadists infiltrating Iraq, the group said, denying that they had taken part in any attacks against US interests or personnel.

"We reserve the legal right to respond to these attacks and hold the perpetrators accountable on Iraqi soil," the Hashed said.

US defence spokesman John Kirby said in a statement that three military facilities used by Iran-backed militia had been hit overnight Sunday to Monday.

- 'Treacherous aggression' -

The strikes targeted operational and weapons storage facilities at two locations in Syria and one location in Iraq, both of which lie close to the common border, the Pentagon said.

Kirby said the targets had been used by "Iran-backed militias that are engaged in unmanned aerial vehicle (UAV) attacks against US personnel and facilities in Iraq".

Kataeb Hezbollah and Kataeb Sayyid al-Shuhada, two Iraqi Shiite armed factions with close ties to Tehran, were among the "several Iran-backed militia groups" that had used the facilities, the Pentagon said.

The Britain-based Syrian Observatory for Human Rights war monitor, which relies on a network of sources inside Syria, said seven fighters were killed in the strikes.

At least six more fighters were wounded and the targets included an arms depot near Albu Kamal, a Syrian border town on the Euphrates river, the Observatory said.

Syria's state-run SANA news agency said one child was killed in the raid but gave few details.

US interests in Iraq, where 2,500 American troops are deployed as part of an international coalition to fight the jihadist Islamic State group, have been targeted in more than 40 attacks this year.

The vast majority have been bombs against logistics convoys, but rocket fire and drones packed with explosive have also been used. Some attacks have been claimed by pro-Iran factions hoping to press Washington into a full withdrawal.

Iraq's foreign ministry said that the government is proceeding with investigations to "prevent any escalation... detrimental to the security and stability of Iraq".

French Foreign Minister Jean-Yves Le Drian reaffirmed "France's support for the stability and sovereignty of Iraq" and denounced the "unacceptable attacks... against the interests of the" anti-IS coalition.

Lebanese pro-Iran Shiite movement Hezbollah said it "strongly condemns the treacherous American aggression that targeted the Iraqi-Syrian border"

"What the US warplanes have done is a blatant attack on sovereignty... the region will not enjoy stability... until US forces are expelled" from Iraq and Syria, it said.

- Nuclear deal -

Some of the militia groups that form the Hashed al-Shaabi have been deployed in Syria over the years to support regime forces and to further Iran's interests in the country.

In February, US strikes on facilities in eastern Syria used by Iran-backed militia groups left more than 20 fighters dead, according to the Observatory.

The latest US strikes come two days after the United States and France warned Iran that time was running out to return to the 2015 nuclear deal, voicing fears that Tehran's sensitive atomic activities could advance if ongoing talks in Vienna drag on.

A return to that accord has been a key Biden promise after the nuclear deal was trashed by his predecessor Donald Trump.

The UN's nuclear watchdog said Friday it had received no reply from Tehran over the possible extension of a temporary agreement covering inspections at Iranian nuclear facilities which expired on Thursday.

Announcement of the strikes came one day before Biden meets at the White House with Reuven Rivlin, president of Israel, a key US ally and Iran's arch foe.