BAGHDAD, Jan 6 (Reuters) - Iraqi Defence Minister Khaled al-Obeidi said on Tuesday that the Iraqi military has started rebuilding after its near total collapse last summer but that the effort is still in its initial phase.

"We are still in the very early steps; some of these steps might be painful, but we must endure," Obeidi said in a televised address on the national holiday Armed Forces Day.

Prime Minister Haider al-Abadi has sacked several dozen commanders and told Obeidi to lead a probe into corruption within the Iraqi military after Islamic State seized vast swathes of territory from Iraqi security forces last summer.

Since then the hardline militants have been pushed out of several districts around Baghdad and near the Iranian border.

Shi'ite militias, Kurdish peshmerga forces and U.S.-led air strikes have played a leading role in Islamic State's military reverses, but the Iraqi army will be needed in the campaign to recapture and hold the remaining territory under its control.

"Changing some military leaders will be the first step towards building a strong army and we will make changes in the entire military pyramid down to the last soldier," Obeidi said on the national holiday commemorating the 94th anniversary of modern Iraqi military's founding.

Rampant corruption was seen as one of the main reasons why the Iraqi army failed to stop Islamic State in battle. Many units were short of weapons or had soldiers listed on paper who were not actually present in the field.

Currently, several Iraqi security officials estimate the number of functioning military forces at between seven and nine divisions. They caution even those divisions are not all operating at full strength.

The Iraqi army had at least 14 divisions on paper before Islamic State toppled the north's biggest city of Mosul and soldiers deserted en masse.

Obeidi also vowed on Tuesday that the Iraqi forces would soon retake the lands they lost in northern Salahuddin and Nineveh provinces. Obeidi highlighted the importance of Mosul.

"We will liberate it with the hard efforts of our armed forces, volunteers and with the aid of our allies."

Earlier in the day, Abadi and Obeidi placed a garland of flowers at Baghdad's Monument to the Unknown Soldier. (Reporting by Saif Hameed, Ned Parker; Editing by Dominic Evans)