Operation Fallujah: US 'officially involved'
The US confirmed it was providing assistance and support to Iraqi forces in their military operations to wrest control of Fallujah from the IS militants.
"American warplanes launched air raids on Daesh sites in Fallujah, US State Department spokesman, Mark Toner said, using the Arabic acronym for IS.
"A group of American advisers are also providing consultation in support of efforts to restore the city," he told a press briefing in Washington.
The briefing followed comments by Iraq's UN refugee organisation, fearing for the fate of civilians trapped in the embattled city.
The assistant representative of the High Commissioner of the United Nations for Refugees (UNHCR) in Iraq, Leila Jane Nassif, expressed "concern for the safety of around 10 thousand families who have not yet been able to leave the city of Fallujah - which is now in a precarious situation".
More than 80 families were able to leave Fallujah successfully, the commission said, indicating that "the escapes, in some cases, involved the loss of lives - including those of women and children".
On Sunday night, Iraqi Prime Minister Haider al-Abadi announced the start of a military operation to retake the city from the Islamic State group, vowing to liberate Fallujah and raise the Iraqi flag.
Just hours after the battle's opening salvos, heavy fighting ensued between Iraqi forces and militants, with Baghdad's troops storming several towns in the area.
Reports suggested the Shahabi, Harariyat and Dowayah towns on the outskirts of Fallujah were liberated by government forces involved in the battle, according to social media users.
Fallujah is an IS stronghold just 50km (30 miles) west of Baghdad, and has been out of government control since January 2014.
The city is "a safe haven for [the Islamic State group], where they can construct their bombs and plan their operations in relatively close proximity to Baghdad", said Steve Warren, the Baghdad-based spokesman for the US-led coalition in Iraq.
Fallujah and Mosul, the capital of the northern province of Nineveh, are the last two major cities IS holds in Iraq.