In the town of Baiji, north of Baghdad, morning air strikes killed at least 19 militants and wounded at least 17, officials said, while further raids in the evening killed six more.
State television said 19 ISIL terrorists were killed in the earlier set of Baiji raids.
In the Husseibah area of Anbar province, west of Baghdad, another air strike killed 13 others, 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 terrorists from the Islamic State of Iraq and the Levant, or ISIL, have overrun major areas of five provinces and driven to within 100 kilometres (60 miles) of Baghdad.
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