Anti-government fighters hoisting a black flag like one often flown by jihadists also seized six army Humvees and set fire to some of them after clashes with security forces near the city, which has been outside of government control for weeks, according to videos posted on YouTube.
The videos -- which could not be immediately verified -- show five soldiers being led away. Some witnesses also spoke of five soldiers "captured" but others said as many as 22 were taken.
One video shows a pick-up truck with five men dressed in Iraqi army uniform sitting in the back as onlookers crowd around them, hoisting the black flag and shouting slogans in support of the al-Qaeda-linked Islamic State of Iraq and the Levant.
Another video shows militants driving two Iraqi army Humvees as Fallujah residents look on.
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Witnesses said six Humvees were seized, and that three were set ablaze.
The latest unrest marks another setback for Iraqi forces who have struggled to wrest back control of Fallujah and parts of nearby Ramadi that have been out of government control for weeks.
Also today, 12 people were killed in violence across the country, pushing the overall death toll for the month above 850, more than triple the toll for January 2013, according to an AFP tally.