Contrary to claims by the Iraqi government, only one third of Fallujah has been cleared of Islamic State (Isis) militants with other parts of the city still being fought over, a senior US military figure has said.

Iraqi prime minister Haider al-Abadi had claimed on Friday (17 June) that the city in Anbar province had "returned to the embrace of the nation," and that the remaining Isis fighters would be defeated "within hours".

Lieutenant General Abdul-Wahab al-Saadi, the Fallujah operation's top special forces commander, said on Monday (20 June) that the offensive had killed 2,500 Isis fighters.

But over the last few days, clashes have continued between the Iraqi army and Jihadi fighters in the northern part of the city.

US Army Colonel, Christopher Garver, said parts of the city were still "contested" and there was stiff resistance against the Iraqi forces as they left the city centre.

"What it looks like is (an IS) defensive belt around the city with not as stiff defences inside. That could be their toughest fighting," he said, according to the Associated Press.

The UN refugee agency said that more than 85,000 people have fled Fallujah and the surrounding area since the offensive began.

Meanwhile, a series of attacks in and around Baghdad, including one targeting anti-Isis fighters, killed at least 12 people and wounded 42 others on Tuesday 21 June.