Anti-government fighters have held Fallujah, just a short drive from Baghdad, and shifting parts of Anbar provincial capital Ramadi, farther west, since early January.
"A military operation was launched... To eliminate the ISIL organisation and liberate Fallujah," a senior army officer said, referring to powerful jihadist group the Islamic State of Iraq and the Levant.
"The operation will continue until an assault on Fallujah," the officer said.
But such an assault is unlikely to occur soon, as security forces have struggled all year to retake territory in Anbar from militants.
Shelling and clashes began in and around Fallujah about 3:00 am (0000 GMT) today and continued for hours, a tribal leader said.
Eight people were killed and nine wounded, according to Dr Ahmed Shami of Fallujah's main hospital
Among the dead were two children, while another two children were wounded, he said.
The crisis in the desert province of Anbar, which shares a long border with conflict-hit Syria, erupted in late December when security forces dismantled Iraq's main Sunni Arab anti-government protest camp just outside Ramadi.
In other violence on Friday, a roadside bomb exploded near an army patrol in Khales, northeast of Baghdad, killing three soldiers and wounding two, a police colonel and a doctor said.
The bloodshed comes during vote counting from the April 30 general election, the first since American troops withdrew in late 2011, and amid a protracted surge in nationwide unrest.
While officials are quick to blame external factors for the violence, analysts and diplomats say widespread anger among the Sunni Arab minority is also a key cause.
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