Clashes between Iraqi tribesmen and the Islamic State group in Fallujah have halted after the jihadists detained dozens of residents of the city west of Baghdad, officials said Sunday.

The fighting between the Sunni Arab tribesmen and IS in Fallujah, one of two cities it still holds in Iraq, challenges the jihadists' ability to maintain control.

But officials said tribesmen were running short of supplies on Saturday, and IS, which is known for its extreme violence, has already executed a large number of opponents elsewhere in Anbar province.

Tribesmen in three areas of Fallujah "withdrew from the clashes (with IS), fearing for the fate of the detainees", an army lieutenant colonel told AFP on condition of anonymity.

"The clashes stopped because of the imbalance of power and fear that the detainees would be executed," said Issa Sayir who was appointed by the Anbar governor to administer the Fallujah area.

Sayir said IS was likely to execute Fallujah residents for their alleged "cooperation with the security forces".

Raja Barakat, a member of the provincial council in Anbar, where Fallujah is located, said: "We now fear that the (IS) organisation will carry out a massacre in the city."

Sayir estimated the number of detainees at around 60, while the lieutenant colonel said the figure was over 110 and a tribal leader said more than 100.

Sheikh Majeed al-Juraisi, a leader in one of the tribes fighting the jihadists in Fallujah, said IS had seized the residents over the previous two days.

- Civilians trapped in city -

"We hold the prime minister responsible for any massacre carried out against the people of Fallujah," Barakat said, calling for the launch of a military operation to retake the city.

Both Sayir and the army officer said a military operation would be launched in the Fallujah area in coming days, but it may come too late for the detainees in the city.

Officials said the clashes began Friday as a fight between tribesmen and Al-Hisba, IS members charged with enforcing the religious strictures of the Sunni extremist group in the city.

The fighting escalated into gunbattles involving members of several tribes.

IS launched a sweeping offensive that overran swathes of Iraq in June 2014, but security forces and allied fighters have pushed the jihadists back with US-led air support.

Fallujah, 50 kilometres (30 miles) west of Baghdad, is the only Iraqi city apart from IS's main hub, Mosul in the north, still under jihadist control.

The militants also hold other areas, including large towns such as Tal Afar and Hawijah.

Anti-government fighters seized Fallujah in early 2014 during unrest that broke out after security forces demolished a protest camp in western Iraq, and it later became an IS stronghold.

The tens of thousands of civilians in Fallujah are facing increasingly dire living conditions, and officials say IS is preventing people from leaving the city, which has largely been cut off by security forces.

There are an estimated 300 to 400 IS fighters inside Fallujah, but the jihadists have repeatedly seized areas and defended others for extended periods despite being heavily outnumbered.