The United Nations has declared its highest level of emergency in Iraq as fresh clashes between government troops and Sunni rebels killed four children west of Baghdad.

Fighting erupted early on Thursday in the rebel-held city of Fallujah, about 65km west of Baghdad.

The clashes on the city's northern outskirts killed four children, along with a woman and at least 10 fighters, said Fallujah hospital director Ahmed Shami.

Fallujah has been in the hands of the Islamic State since early January, when the group seized much of Western Anbar province along with parts of the provincial capital of Ramadi.

The fighting came as the UN declared the situation in Iraq a "Level 3 Emergency" - a development that will trigger additional goods, funds and assets to respond to the needs of the displaced, said UN special representative Nickolay Mladenov, pointing to the "scale and complexity of the current humanitarian catastrophe."

The Security Council also said it was backing a newly nominated premier-designate in the hope that he can swiftly form an "inclusive government'' that could counter the threat from rebels, which has plunged Iraq into its worst crisis since the US troop withdrawal in 2011.

Tens of thousands of Yazidis fled the Islamic State group's advance to take refuge in the remote desert Sinjar mountain range.

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The US and Iraqi military have dropped food and water supplies, and in recent days Kurds from neighbouring Syria battled to open a corridor to the mountain, allowing some 45,000 to escape. 

On Thursday, President Barack Obama said the US had broken the siege on Sinjar Mountain, but that airstrikes would continue.

Speaking at Martha's Vineyard in Massachusetts, Obama said US operations helped thousands of civilians flee down the mountain, and that it was unlikely that more airdrops of food and water would be needed.

The UN said it would provide increased support to those who had escaped Sinjar and to 400,000 other Iraqis who had fled since June to the Kurdish province of Dahuk. Others have fled to other parts of the Kurdish region or further south.

A total of 15 million have been displaced by the fighting since the rebels captured Iraq's second-largest city, Mosul, in June and quickly swept over other parts of the country.

The United States has been carrying out airstrikes in recent days against Islamic State fighters, helping fend back their advance on Kurdish regions.

Source: Agencies