Fallujah is one of two Iraqi cities still controlled by IS, and a concerted and sustained uprising by local tribes could pose a significant threat to the estimated 300 to 400 jihadists inside it.
Sunni Arab tribesmen from Anbar province, where Fallujah is located, played a key role in driving back IS's predecessor organisation Al-Qaeda in Iraq after joining forces with US troops from 2006.
The Friday Fallujah shootout pitted fighters from the Al-Juraisat, Al-Mahamda and Al-Halabsa tribes against the jihadists.
The initial fighting broke out between tribesmen and IS members known as Al-Hisba, who are responsible for enforcing religious strictures in the city, officials said.
According to a police colonel, the fighting was ongoing in central and northern Fallujah as of Friday evening, and tribesmen torched an IS checkpoint on the outskirts of one northern area.
Issa Sayir, who was appointed by the Anbar governor to administer the Fallujah area, said the fighting began in Al-Jolan on the northwest side of the city, then spread to Nazal in its centre and Al-Askari on its eastern side.
Anbar provincial councillor Raja al-Barakat also said the unrest had spread to Nazal and other areas, and that the tribesmen urgently needed air and ground support.
Sayir said the gun battle reflected tensions resulting from increasingly difficult living conditions caused by Fallujah's isolation by the security forces.
Conditions in Fallujah are dire, with Anbar Governor Sohaib al-Rawi saying that the situation "has reached a state of famine".
Years outside government control
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A police lieutenant colonel gave a different account of the start of the fighting, saying it began after Al-Hisba members accused a woman in Al-Nizaiza market in central Fallujah of misconduct because she had failed to cover her hands with gloves.
Sheikh Majeed al-Juraisi, a leader of the Al-Juraisat tribe, described the clashes as an uprising against IS in the city and called on the government and security forces to help residents who are fighting the jihadists.
Juraisi said that tribesmen seized part of Al-Jolan area.
The interior ministry also said earlier in the day that tribesmen had seized parts of Al-Jolan and its outskirts but that IS later regained control.
Citing intelligence information, the ministry said the clashes began as a fight between Al-Juraisat tribesmen and the Al-Hisba in Al-Nizaiza market.
It escalated into a shootout in which light and medium weapons were used, and Al-Mahamda and Al-Halabsa tribesmen backed Al-Juraisat fighters, the ministry said.
Fallujah, which is located about 50 kilometres (30 miles) west of Baghdad, is the only Iraqi city apart from IS's main northern hub Mosul still under jihadist control.
Tens of thousands of civilians are estimated to be still inside Fallujah.
Anti-government fighters took control of the city in early 2014 during unrest that broke out after security forces demolished a protest camp farther west, and has become a key IS stronghold.
IS launched a sweeping offensive that overran large areas north and west of Baghdad in June 2014, but security forces and allied fighters have pushed the jihadists back with support from US-led air strikes.
Tribesmen have played a key role in holding the jihadists back in multiple areas, including Haditha in Anbar, Amerli in Salaheddin province and Dhuluiyah in Diyala.