Pro-Iranian militias exchanged fire with a US-led coalition in eastern Syria Monday, a war monitor and the coalition said, in an escalation after deadly US airstrikes in Iraq and Syria the previous night. 

US forces "were attacked by multiple rockets" in eastern Syria, but there were no casualties and personnel "conducted counter-battery artillery fire at rocket launching positions", said coalition spokesman Wayne Marotto on Twitter.

The Syrian Observatory for Human Rights war monitor reported shellfire by Iran-backed militias against the US base in eastern Syria's Al-Omar oil field, and said the coalition fired heavy artillery at the militia-controlled town of Al-Mayadeen in response.

The exchange of fire came just hours after Secretary of State Antony Blinken declared that US airstrikes on pro-Iran fighters in Iraq and Syria on Sunday night sent a "strong message" not to keep attacking US forces in Iraq.

The US airstrikes were the second such deadly raid on pro-Iran targets since US President Joe Biden took office, and have sparked fears of a new US-Iran escalation amid faltering efforts to revive Tehran's 2015 nuclear deal with world powers. 

"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... 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.

Iraq's Prime Minister Mustafa al-Kadhemi decried the strikes as an "unacceptable violation of Iraqi sovereignty and Iraqi national security", while Damascus condemned a violation against both nations.

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 and warning they had "the legal right to respond... and hold the perpetrators accountable on Iraqi soil".

The Pentagon said the strikes targeted operational and weapons storage facilities at two locations in Syria and one in Iraq, all near the common border, used by militias engaged in drone attacks against US interests in Iraq.

- 'Flagrant violation' -

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

The Observatory, which relies on a network of sources inside Syria, said seven fighters were killed in the strikes and at least six more were wounded.

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, while its foreign ministry condemned the raid as "a flagrant violation of the sanctity of Syrian and Iraqi territory".

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, leaving Baghdad -- which counts both Washington and Tehran as allies -- caught in the middle. 

Iraq's foreign ministry said that the government was proceeding with investigations to "prevent any escalation", while Kadhemi re-emphasised his country's "refusal to be an arena for settling scores".

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

Lebanese Shiite movement Hezbollah "strongly" condemned the air strikes.

"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, the pro-Iran group said.

- Nuclear talks wobble -

Some of the militia groups that form the Hashed al-Shaabi have been deployed in war-torn 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 days after the US 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 talks in Vienna drag on.

A return to that accord has been a key focus for Biden after the nuclear deal was trashed by his predecessor Donald Trump, who also imposed devastating new sanctions on Iran.

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 a day earlier.