Tikrit, Iraq (CNN) While Iraqi government and allied forces were on the defensive Friday in Ramadi, they remained on the offensive in Tirkit -- trying to win over not only the strategic city, but the hearts and minds of its nearby residents.

Iraqi forces steadily bombarded the last part of Tikrit still controlled by ISIS, with fighting described by one wounded man as intense. Still, even as it fends off this assault, the militant group continues with its barbaric tactics.

"Yesterday, bodies floated down the (Tigris) River from the hospital," said Saber Kraidi, an eight-year Iraqi military veteran. "They were people from Tikrit executed by ISIS."

The Iraqi military is joined by some Sunni fighters and a predominantly Shiite militia, working together to retake the city best known to most Westerners as the hometown of former dictator Saddam Hussein

They are working on not just winning the battle, but securing the peace. Members of the Badr organization, a powerful Shiite armed group, handed out food and supplies Friday to residents of the Sunni village of Albu Safah, whose 30 families have been holed up the last 10 months amid the fighting.

The village's leader, Haji Jamid, said the Shiite fighters' efforts were working.

"They're good," Jamid said. "If someone is sick, they'll take them to the doctor, even at 2 or 3 in the morning.

"If it weren't for them, ISIS would have slaughtered us."

After Tikrit, will Mosul be next?

In June, Tikrit fell to ISIS, which has conquered large areas of Iraq and Syria and claimed them as part of its Islamic caliphate. There have several attempts to take it back since then, all of them failures.

The latest push began this month, involving around 30,000 fighters.

By Thursday, the government controlled about 75% of the besieged city, with about 150 holdout ISIS fighters controlling the rest, said Main Al-Kadhimi, commander of the Hashd Al-Shaabi militia.

There was no independent confirmation of such a significant advance by the Iraqi forces. But they have been making progress in recent days.

That includes gaining control of Tikrit Military Hospital, a few blocks south of the presidential palace, on Wednesday.

The goal is that, if Iraqi and allied forces can take Tikrit, then they'll have more realistic hope of similarly winning back Mosul -- a city that's nearly 10 times bigger.

ISIS assaults Ramadi

Yet, even if ISIS is losing ground in Tikrit, that doesn't mean it's not a dangerous, destructive force elsewhere.

Case in point is happening about 100 miles south of Tikrit in Ramadi, which the extremist group began assaulting on Wednesday. Faleh al-Issawi, deputy head of the Anbar provincial council, has said officials believe the Ramadi assault "is an ISIS response to the Tikrit operation."

More than 40 Iraqi soldiers died when ISIS blew up the Iraqi army headquarters near Ramadi in Iraq's western Anbar province, an Anbar provincial leader told CNN on Friday.

ISIS fighters there dug a tunnel underneath the army headquarters and detonated hundreds of homemade bombs, Sabah Al-Karhout, the head of the Anbar Provincial Council, said Thursday. The headquarters are located in the Albu Diab area, just 4 kilometers (2.5 miles) north of Ramadi.

Al-Karhout denied reports that the U.S.-led coalition had bombed the headquarters. So, too, did the U.S. government, with its Baghdad embassy stating Friday that no coalition aircraft were even in the area

A statement released early Friday by the U.S.-led coalition against ISIS said the Iraqi security forces had successfully repelled the ISIS attack on Ramadi, despite coming under attack from several directions.

"The successful defense of Ramadi by Iraqi Security Forces is another example of their increasing ability to defeat Daesh in multiple locations and prevent the terrorist group from gaining ground," said Lt. Gen. James L. Terry, the coalition force's commander, using another name for ISIS.

"The ISF continues to hold terrain in some locations while making gains in others."

In an audio message posted Thursday, ISIS spokesman Abu Mohammed al Adnani called reports of victories by coalition members against the extremist group "delusional and fake."

He spoke of the coalition's use of fighter jets, heavy artillery and tanks, saying it is a "nightmare and will go eventually."