(CNN) -

The extremist group that's taken over a large swath of western and northern Iraq announced on Sunday the establishment of a "caliphate," an Islamic state stretching across the region, and said it would now be known as the Islamic State rather than the Islamic State of Iraq and Syria.

The announcement was made in a newly released audio message and written statement purportedly from the official spokesman of ISIS, Abu Mohammed al-Adnani al-Shami.

He said "Al-Baghdadi" is the emir of the caliphate, using his real name Ibrahim Awwad Ibrahim Ali al-Badri al Samarrai, but who is more commonly known as Abu Bakr al-Baghdadi.

The group said its flag flies from the Aleppo province in Syria to Diyala province in Iraq.

The murky battle for Tikrit

Iraq's government is touting military offensive to recapture Saddam Hussein's hometown of Tikrit from extremists, with some officials taking to state-run television over the weekend to declare the army had defeated the Islamic State of Iraq and Syria.

But those who live in the city nestled along the Tigris River, about 140 kilometers (about 87 miles) northwest of Baghdad, told a different story on Sunday.

"There are no Iraqi troops here," one woman told CNN by telephone from Tikrit. The only presence, at least in her neighborhood, is the "Islamic state," she said, referring to ISIS.

The woman in Tikrit, who asked not to be identified over concerns for her safety, said she could hear the sounds of a fierce battle, in the form of shelling, being carried out by both sides.

A video posted on YouTube appears to support her assertion. In it, a man gives a tour of the city to show, he says, that there were no Iraqi security forces on the streets on Saturday -- the day Iraqi forces said they launched the offensive.

On the video, the man can be heard repeatedly saying "June 28, 2014," presumably to offer evidence of the date.

The man says "Thank God, Tikrit is safe and still in the hand of tribesmen and not troops of 'al-Haliki,'" a derogatory reference to Prime Minister Nuri al-Maliki that refers to his death.

The video also shows a concrete blast wall erected around government buildings being taken down.

Witnesses inside and outside of Tikrit said Iraqi forces were heavily shelling the city.

At the same time, state-run Iraqi TV showed video footage of large plumes of black smoke billowing from the city. Another video, released by the Ministry of Defense, showed Iraqi troops and convoys loaded with heavy weapons driving through the desert. The video was titled "cleansing the road between Samarra and Tikrit."

CNN cannot independently confirm the claims.

Clashes south of Kirkuk

Fighting erupted Sunday between Shiite militiamen and Sunni militants believed to be ISIS fighters in a village about 30 kilometers south of the oil-rich city of Kirkuk, police officials told CNN.

About 100 Shiite militants backed by Turkmen fighters attacked the village of al-Basheer, which was seized two weeks ago by ISIS fighters, the officials said.

At least 12 Shiite militia fighters were killed and eight others were wounded in the fighting that lasted for several hours. Sporadic clashes continued to be reported into the evening.

Al-Basheer has a mixed population of Shiite Turkmen and Sunnis.

Fighting in Jalawla

Members of the Kurdish fighting force -- known as Peshmerga -- battled ISIS fighters near the town of Jalawla, about 85 kilometers (53 miles) north of Baghdad, on Sunday, police officials told CNN.

The fighting was still ongoing, the officials said.

Jalawla is under the control of the Peshmerga, but ISIS controls al-Saadiya about 15 kilometers (9.3 miles) to the south.