QUSH TAPA, Iraq — The Iraqi military command has begun a campaign to re-enlist soldiers and officers who abandoned their units, a crucial step in its effort to rebuild an army that has been routed in battle after battle by Islamic State jihadists.

Even as the government has continued to equip volunteers, the de facto amnesty for deserters is an acknowledgment that the army desperately needs experienced soldiers — even ones who ran — for a force that is sustaining heavy losses despite the American-led airstrike campaign against the Islamic State, also known as ISIS.

Army officials at re-enlistment centers in Baghdad and in the northern Kurdistan region say they have seen some success in the effort. More than 6,000 soldiers and officers, including those who were sent home by their commanders as well as those who fled unilaterally, had registered at a military outpost here in Kurdistan, and more than 5,000 had signed up in Baghdad, officials said.

But the returning troops make up only a small part of what has been lost. In June, when Islamic State fighters swept across northern Iraq from Syria, four Iraqi divisions disintegrated, accounting for roughly 30,000 troops, though it remains unclear how many were killed and how many retreated on their own or under orders. Some units abandoned their weapons and equipment to the advancing insurgents.