Iraqi army was mostly less upbeat, with one senior officer saying he could envision the battle of Tikrit lasting two more weeks.
Saadi said he thought the reason there had been no coalition air strikes on Tikrit was political, not military.
Iran has been Baghdad’s main foreign partner in the operation and Tehran’s top commander in charge of external operations, Qassem Soleimani, has been omnipresent on the front lines.
Officials in Washington have expressed unease at the level of Iranian involvement in Tikrit dictator Saddam Hussein’s hometown.
Coalition air strikes have supported several other operations to reclaim Jihadist-held territory in Iraq in recent months, including some in which Iran-backed militias were involved.
Iraqi security forces, backed by volunteers and militias, and in some cases tribesmen opposed to IS, have in recent months been working their way north.
In October, they retook Jurf al-Sakhr, the southernmost area to have been captured by IS, and have since also reclaimed the eastern province of Diyala.
Iranian support was crucial in both those operations.
Kurdish peshmerga have also been pushing back Jihadists from northern parts of the country, with US-led coalition support.
The last remaining IS stronghold east of the Tigris river is Hawijah, a city northeast of Tikrit, where fleeing Jihadists are believed to have gathered and on which Kurdish forces are advancing.
Tikrit is seen by commanders as a key stepping stone on the way to reconquering IS’s northern hub of Mosul, Iraq’s second city.
The outcome of the battle seems in little doubt but there is more at stake for the government than just territorial gain.
The vast operation is seen as a test of Baghdad’s ability to instil discipline in the array of fighting forces involved in the anti-IS war and prevent some of the abuses committed in past operations.
Tens of thousands of people have been displaced by the offensive. Tikrit once had an estimated population of 200,000 but it is unclear how many civilians remain in the war-torn city.
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