Reports from medical officials at the provincial hospital in Tikrit said that ISIS had begun evacuating its wounded from the site on Friday.

ISIS, however, claimed a victory over government forces at the southern gates of the city, in postings on Twitter accounts associated with the extremists.

In other clashes, like the battle for control of the important Baiji refinery in Salahuddin Province, both sides have sometimes traded control of contested territory on an almost daily basis.

“The signs of success are clear, and there is a very big change in the performance of the security forces, and now we can say the initiative is in the hands of the Iraqi forces,” said Ahmed al-Sheraifi, a former air force pilot and now a professor at Baghdad University.

Mr. Sheraifi attributed the improved performance to intelligence support contributed by American drones, which have begun flying over Iraq, as well as to American advice on tactics. “The security forces began relying on their airborne division, and this is a trademark of U.S. tactics,” he said.

The Iraqi Army’s counteroffensive began Thursday with an airborne assault on the campus of Salahuddin University, which drove the militants out of that site. Early Saturday morning, after two days of fighting around the university, in downtown Tikrit, the Iraqi Army launched a three-pronged attack, with a large body of ground troops driving into the city from the south and east, joined by troops garrisoned in Camp Speicher, north of the city, an Iraqi Air Force training base that never fell to the insurgents.

It appeared that the offensive in Tikrit was costly to both sides, with ISIS planting bombs along the highways leading to the city, and sending suicide bombers against Iraqi armored vehicles. The militants, in their Twitter posts, admitted to losing 30 fighters, but also claimed to have destroyed eight Iraqi tanks with suicide attacks. General Atta claimed that Iraqi forces had killed 29 of the extremists in Tikrit.