Further rocket attacks by Iran-backed groups took place late Friday, prompting more strikes by coalition warplanes, the Syrian Observatory for Human Rights reported.

Washington carried out the initial strikes after the Pentagon said a US contractor died -- and another contractor and five military personnel were wounded -- by a drone "of Iranian origin" that struck a US-led coalition base near Hasakeh in northeastern Syria on Thursday.

US Defense Secretary Lloyd Austin said that, at President Joe Biden's direction, he had ordered the "precision air strikes... in eastern Syria against facilities used by groups affiliated with Iran's Islamic Revolutionary Guard Corps".

On Saturday, the Britain-based Observatory said 19 people were killed in the first wave of US strikes: three Syrian regime soldiers and 16 members of Iran-backed forces, including 11 Syrian nationals.

Following the strikes, Biden sought to lower the temperature saying the United States "does not seek conflict with Iran, but is prepared to act forcefully to protect our people".

More rocket attacks

Hours after the strikes, 10 rockets were fired at American and coalition forces at the Green Village base in northeast Syria, the US Central Command (CENTCOM) said.

There were no injuries or damage to facilities at the base, but one rocket struck a home around five kilometres (three miles) away, causing minor wounds to two women and two children, CENTCOM added.

The militias later Friday targeted a base in the Conoco gas field, prompting retaliatory strikes from coalition warplanes on targets in Deir Ezzor city, the Observatory said.

The war monitor said rocket fire then targeted coalition facilities at the Al-Omar oil field base and in the eastern countryside of Deir Ezzor, "causing material damage".

A "cautious calm" returned to the Deir Ezzor area in the early hours of Saturday morning, the Observatory said.