The United Nations expressed concern about some 50,000 people still in Falluja as Iraqi government forces clashed with Islamic State militants near the city, a UN spokesman said on Monday.

Iraqi Prime Minister Haider al-Abadi on Sunday announced the launching of an offensive to retake the Islamic State stronghold of Falluja after the military told residents to leave before fighting started.

"We're very concerned about the fate of the civilians that remain in Falluja as the military operations are undertaken," UN spokesman Stephane Dujarric told reporters.

"Our estimate is that there are around 50,000 civilians in Falluja," he said. "The humanitarian situation obviously remains very fluid."

The UN estimate of 50,000 civilians in Falluja is lower than an Iraqi figure, and slightly below a recent US military estimate of 60,000 to 90,000. About 300,000 people lived in the Euphrates River city before the current war.

Iraqi forces have surrounded Falluja since last year but focused most combat operations on IS-held territories further west and north. The authorities have pledged to retake Mosul, the north's biggest city, this year in keeping with a US plan to oust IS from their de facto capitals in Iraq and Syria.

Dujarric said the United Nations was working with local humanitarian partners to assess the needs and pattern of movement of civilians still in Falluja, a bastion of Sunni Muslim jihadists 50 km (30 miles) from Baghdad that was the first city to fall to Islamic State in January 2014.

"Civilians are under great danger as they try to flee," he said. "It's important that they have some safe corridors."

One of the biggest problems facing fleeing civilians, Dujarric added, is the rising temperatures in Iraq and the risk of dehydration.