BAGHDAD, Iraq (CNN) -

Iraq's semi-autonomous Kurdish region has put tight restrictions on the border crossings used by Iraqis fleeing extremist militants and airstrikes in the northern city of Mosul on Saturday, raising fears of a humanitarian crisis as some desperate families may be left with nowhere to go.

The Kurdish regional government's decision to first close the border crossings and then reopen them with restrictions came on the same day Iraq's security forces went on the offensive, carrying out airstrikes in Mosul and fighting to take back Tikrit from Islamic State of Iraq and Syria fighters, known as ISIS.

The offensive appeared to mark a turn for Iraqi security forces, who were routed by ISIS fighters this month during a lighting advance that saw the al Qaeda offshoot seize large swaths of northern and western Iraq.

State media and a local tribal leader reported that Iraqi forces had retaken the city of Tikrit, Saddam Hussein's hometown.

Sheikh Khamis al-Joubouri, a key tribal leader in Tikrit, told CNN that the Iraqi security forces entered the city supported by special forces and fighters from among the local tribes, and had gained control.

He said ISIS fighters retreated in the direction of Kirkuk and Nineveh provinces.

However, amid claim and counter-claim, a combatant told a CNN freelance reporter that ISIS fighters remained in control of Tikrit, but that there are fierce clashes in an area about 20 kilometers from the city center, toward Samarra.

State-run Iraqiya TV reported that the Iraqi army and volunteer militia groups had cleared ISIS fighters from the city, having advanced on the city from four directions.

Sabah Numan, a Counter Terrorism Unit spokesman, told the station that 120 militants had been killed and 20 vehicles destroyed in a large-scale operation that began Saturday morning.

He did not provide any evidence of the claim, and CNN cannot independently confirm the reports.

Sunni tribes wade into fight

Al-Joubouri said that the tribes were not aligned with the government or with ISIS and had stayed out of the fight until now.

But, he said, when ISIS fighters who arrived in Tikrit robbed banks and carried out executions, as well as bringing the local economy to a standstill, the tribal leaders offered their help to the Iraqi security forces poised outside the city. The tribal leaders shared their knowledge of the city, including routes and known ISIS positions, he said.

On Friday, Human Rights Watch reported that two mass graves believed to contain the bodies of Iraqi soldiers, police and civilians killed by ISIS and their militant allies had been discovered in Tikrit.

Iraq's military spokesman, Maj. Gen. Qassim Atta, told a news briefing Saturday that Iraq's forces had regained the upper hand against ISIS and were now being supported by the tribes.

"We are advancing in all our fights," he said.

As part of that fight, Iraqi security forces broke up a terror cell in the predominantly Sunni neighborhood of al-Amiriya in eastern Baghdad, the Ministry of Defense said. Nine people were arrested following a raid Friday on a Sunni mosque where the ministry claims security forces uncovered cache of weapons and bombs.

After being interrogated, those detained admitted they planned to carry out attacks during the holy month of Ramadan, which begins Sunday, the ministry said.

Additionally, Iraqi airstrikes targeted ISIS fighters building an earthen dam along the Euphrates River in Anbar province.

Families flee

Iraq's air force carried out a series of airstrikes on Mosul, according to a senior Iraqi military official.

The airstrikes targeted four locations inside Iraq's second-largest city, including ISIS headquarters, said Mazen al-Safaar, a traffic director in Mosul.

But a doctor says the airstrikes also hit Mosul's administration building and the Old City's shopping district.

At least seven civilians were killed and two were wounded in the airstrikes, according to Dr. Salaheldin al-Naimi, the director of the health administration.

Hundreds of thousands fled when Mosul fell to ISIS two and a half weeks ago. Many headed for Kurdish-controlled areas.