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 air strikes 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 shell fire 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 air strikes 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 air strikes 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.