In the town of Baiji, north of Baghdad, air strikes killed at least 19 people and wounded at least 17 others, officials said.
The officials said the dead and wounded were civilians, and it was unclear if there were any casualties among the militants who were the target of the strikes.
Iraqiya state television said 19 "terrorists" were killed in the Baiji raids.
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In the Husseibah area of Anbar province, west of Baghdad, another air strike killed seven militants and six civilians, witnesses said.
Elsewhere in Anbar, security forces and allied tribesmen held off an assault on the strategic town of Haditha, located on the road to provincial capital Ramadi, a police officer said.
Militants also launched a renewed push to seize Iraq's largest oil refinery, which is located near Baiji, but the overnight attack was repelled by security forces, officials said.
The refinery, which filled some 50 percent of Iraq's demand for refined petroleum products in better days, has been the scene of heavy fighting since militants launched a major offensive on June 9, sending jitters through world oil markets.
The militants, led by jihadists from the Islamic State of Iraq and the Levant, or ISIL, have overrun major areas of five provinces and driven to within less than 100 kilometres (60 miles) of Baghdad.
Security forces performed poorly during the initial onslaught, and are now struggling to hold their ground in the face of the relentless militant push.
