BAGHDAD, Iraq (CNN) -

Iraq's government touted its 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 extremist group on Sunday announced the establishment of a "caliphate" and the renaming of the Islamic State in Iraq and Syria (ISIS) to the "Islamic State" 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 new caliphate, using his real name of Ibrahim Awwad Ibrahim Ali al-Badri al-Samarrai, but who is more commonly known as Abu Bakr al-Baghdadi.

The group's statement said its flag flies from Aleppo province in Syria to Diyala province in Iraq.

It is also called on Muslims to swear allegiance to the caliphate, which means Islamic state.

CNN could not independently verify the authenticity of the message.

Witnesses: Heavy shelling in Tikrit

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.

Two days ago, the air force dropped leaflets from helicopters, demanding resident leave the city "for their safety."

A large number of people have fled Tikrit for smaller villages to the north, according to witnesses, who say Iraqi forces are battling ISIS on the southern edge of 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.

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