There was no independent verification of the toll among the militants, said to be members of the Islamic State of Iraq and the Levant (ISIL), a jihadi group also fighting in the civil war in neighbouring Syria. (Agencies)
ISIL militants and other Sunni groups angered by the Shi'ite Muslim-led Baghdad government overran Falluja and parts of the nearby city of Ramadi in the western province of Anbar on January 1.
The Defence Ministry statement said most of the 57 militants had been killed in the outskirts of Ramadi, but gave few details.
Prime Minister Nuri al-Maliki has held back from an all-out assault on Falluja to give time for a negotiated way out of the standoff, but mediation efforts appear to have failed.
Troops intensified shelling of Falluja late on Sunday and security officials said a ground assault would follow soon.
"The assault has to take place on Falluja, sooner or later," said a top security official directly involved in dealing with the stand-off. "The time for talking ran out."
The official said the army was tightening its siege of the city and would continue shelling it for at least three days to weaken militant positions and drive remaining residents out.
"We will not enter as long as there are civilians inside," the official told Reuters on condition of anonymity. "We want them to leave, and they will leave under the pressure of daily bombardment."
A resident of Falluja said many families had moved to the city's western districts because other areas were being shelled, and the army was fighting militants in the north.
Maliki has appealed for international support and weapons to fight al Qaeda, although critics say his own policies towards Iraq's once-dominant Sunni community are at least partly to blame for reviving an insurgency that had climaxed in 2006-07.
Last year was Iraq's bloodiest since 2008, according to the United Nations, and the violence monitoring group Iraq Body Count has said more than 1,000 people were killed in January alone.
Six bombs targeting Shi'ite areas of Baghdad province killed at least 20 people on Monday, police said. Two of the bombs blew up in the town of Mahmudiya, about 30 km (20 miles) south of Baghdad, killing eight people. Two more blasts occurred in the capital.
Separately, police said they found the bodies of four people, one of them a woman, who had been shot in the head or chest in southwestern Baghdad.
Two soldiers were killed in clashes with gunmen in Baquba, a city 65 km (40 miles) northeast of Baghdad, a military source said.
No group has claimed responsibility for Monday's attacks but Shi'ites are often targeted by Sunni militants who have been regaining strength, especially in Anbar, which borders Syria.
Al Qaeda said on Monday it had no links with ISIL, a group whose precursors fought U.S. troops in Iraq and which is now playing a powerful but divisive role in Syria's civil war, as well as driving the insurgency in Iraq.
There was no independent verification of the toll among the militants, said to be members of the Islamic State of Iraq and the Levant (ISIL), a jihadi group also fighting in the civil war in neighbouring Syria.