Fewer than 1,000 Islamic State fighters remain in Iraq and Syria, the United States-led international coalition fighting the hardline Sunni militant group said on Wednesday, a third of the estimated figure only three weeks ago.

The figure excludes areas in western Syria under the control of President Bashar al-Assad's government and his allies.

Assad's main ally Russia also said on Wednesday the main battle with Islamic State in Syria was over. Foreign Minister Sergei Lavrov said the key task in Syria was now destroying another Islamist group, the Nusra Front.

The US-led coalition had said on December 5 that there were fewer than 3,000 fighters remaining. Iraq declared 'final victory' over the group on December 9.

Most of the fighters had been killed or captured over the past three years, the coalition said on Wednesday. It would not respond to a question on whether some fighters could have escaped to other countries, saying it would not 'engage in public speculation' but said it was working on preventing that.

'We can tell you that we are working with our partners to kill or capture all remaining ISIS terrorists, to destroy their network and prevent their resurgence, and also to prevent them from escaping to bordering countries,' it said.