Only 400 soldiers are left on Thursday, following the mass walkout over terrible pay and conditions.
Salaries in the new army range from $50 a month to $180 for a colonel, a US occupation administration source said.
Speaking on condition of anonymity, the official also confirmed there had been discipline problems – with some recruits refusing to obey instructions before resigning.
"My understanding is that they felt they should be paid more money, for example, than the police," he said, adding that the occupation administration will review all security force salaries.
Iraq’s administrators had been building a new Iraqi army after dismissing all the members of Saddam Hussein's armed forces following the invasion in April.
"There may have been some confusion when they first joined the Iraqi army. They weren't sure exactly what their terms and conditions are," the official said.
What remains of the Iraqi First Battalion is serving with the US 4th Infantry Division.
The official said a second Iraqi battalion is now training "and there are no resignations from that."
Another group of more than 2000 recruits are expected to begin their training next year, he said.