"Daesh is not defeated with the liberation of Raqa. The defeat of Daesh was not completed with the liberation of Mosul" in Iraq, British Major General Rupert Jones told reporters, using an Arab acronym for IS.
Speaking in the town of Ain Issa 50 kilometres (30 miles) north of Raqa, Jones said: "We know as an international coalition there's still a great deal more to do here in Syria."
"We will continue to work with the Syrian Democratic Forces to complete the defeat of Daesh," Jones said.
The US-backed forces have successfully routed IS from several areas in Syria since their creation in 2014.
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They have spent months encircling Raqa, the de facto capital of IS's Syrian territory since 2014, and finally broke into it in early June, seizing several neighbourhoods.
But for the past week they have encountered fierce resistance from the jihadists, and progress has also been hampered by the presence of civilians trapped in Raqa city centre.
He also said the "protection of civilians" was of key concern to the coalition.
According to the coalition, 603 civilians have been killed in US-led strikes on Iraq and Syria since the air campaign against the jihadists was launched towards the end of 2014.
But Airwars, a London-based collective of journalists and researchers that tracks civilian deaths in Iraq and Syria, says 744 civilians were killed in coalition strikes in Syria and Iraq in the month of June alone.