Military spokesman Lt. Gen. Qassim al-Moussawi said 50 militants were killed in the fighting. The toll could not be independently verified.
North of Tikrit, government airstrikes hit around eight vehicles carrying militants trying to capture Iraq's largest oil refinery, said Sabah al-Nuaman, the spokesman for Iraq's counterterrorism services. He reported as many as 30 insurgents were killed.
Fighters from the Islamic State group have been trying for weeks to capture the Beiji facility, some 250 kilometers (155 miles) north of Baghdad. The group appeared on the verge of taking the refinery last month, but military troops managed to hold on and have since received reinforcements.
Al-Nuaman also said a helicopter gunship attacked a house in the town of Qaim near the Syrian border where a gathering of the Islamic State group's local leaders was taking place. He said there were several casualties.
The militants seized Qaim, which controls a border crossing with Syria, last month. They now hold a vast stretch of territory straddling the border between the two countries.
The Islamic State group is led by an Iraqi known as Abu Bakr al-Baghdadi, who this week declared the establishment of an Islamic state, or caliphate, in the land the extremists control.
In Syria, where al-Baghdadi's fighters have thrived amid the country's civil war, the group seized the al-Tanak oil field Friday near the border as they try to consolidate their hold along the length of the Euphrates River stretching through Syria and Iraq, according to the Britain-based Syrian Observatory for Human Rights.
The seizure followed the Islamic State group's takeover of Syria's largest oil field on Thursday. Both oil fields were taken from other rebel groups.
Also Friday, more than 40 Indian nurses who were trapped in territory captured by al-Baghdadi's group were released and crossed into Iraq's largely autonomous Kurdish region, authorities said.
They will be flown to India on an aircraft arranged by their government, said Oommen Chandy, chief minister of India's Kerala state.
Associated Press writers Muneeza Naqvi in New Delhi and Bassem Mroue in Beirut contributed to this report.