Sabah Noori, spokesman for Iraq's Counter-Terrorism Service, said its forces had killed 52 jihadist militants in fighting on Sunday and Monday in Anbar provincial capital Ramadi.
"During an operation to clear areas of Ramadi, our forces were able to kill 52 terrorists" from militant group of Islamic State of Iraq and the Levant, Noori said.
The dead included foreign militants, he said, adding that operations to retake some areas of the city were still ongoing.
The crisis in Anbar province erupted in late December when security forces dismantled anti-government protest camp just outside Ramadi.
It is the first time foreign backed militant groups have exercised such open control in major cities since the peak of the deadly violence that followed the US-led invasion of 2003.
More than 370,000 people may have been displaced by violence in Anbar, according to the United Nations.
Violence in other areas of Iraq killed 10 people on Monday.
In the deadliest incident, a mortar round struck a house in Fallujah, killing two women and two children.
The source of the fire was not immediately clear.
In Baghdad, a bomb exploded in a market, killing one person and wounding five, while gunmen shot dead a policeman in Abu Ghraib, west of the capital.
And attacks in the northern province of Nineveh -- one of the most dangerous areas of the country -- killed four people, including a lawyer and a policeman.
Violence has killed more than 1,740 people since the beginning of the year, according to AFP figures based on security and medical sources.
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