A significant number of Islamic State group fighters have withdrawn from northern Iraqi cities, after government forces launched a major ground and air offensive, officials in Tikrit and Mosul said.

"We are hearing reports that fighters are retreating but it is expected to be a fierce battle," Al Jazeera's Jane Arraf, reporting from Baghdad, said on Tuesday.

"But this is battle likely to last days," our correspondent said.

Sources told Al Jazeera that security forces had entered the outskirts of Tikrit and were backed by air, mortar and artillery fires targeting several positions in Tikrit, which has been under Islamic State control for months.

It was not clear if the air strikes were carried out by US or Iraqi jets, however US aircraft have been dropping leaflets warning residents of the impending bombing of Islamic State sites.

Our correspondent cautioned it would be "incredibly difficult" for the government forces to drive out the Sunni armed group from cities that are also dominated by Sunnis.

"I would not claim victory quite so fast, if I were the Iraqi government. They are simply not ready," Arraf said.

Earlier, government forces led by Kurdish fighters and backed by Shia armed volunteers regained control of the towns of Sulaiman Bek and Amerli, driving out the rebel Sunni fighters and liberating the towns under siege for weeks.

Al Jazeera's Sue Turton, who reached Sulaiman Bek, described it as a "ghost town".

However, as aid trickles, people are worried that many Islamic State fighters may have "blended back into the surrounding communities," Turton said.

The Islamic State has declared a "caliphate" in regions under its control in Iraq and Syria, and has engaged in mass killings as it swept through swathes of territories north of Baghdad in June.

Al Jazeera