New Jersey padded its Medicaid bills by $600 million over a dozen years by seeking reimbursement for public worker pensions that the state never paid and inflating the pay rates, according to an Inspector General audit.

The audit instructed the Christie administration to refund at least $300 million of the Medicaid funding it wrongly collected billing for medical and therapeutic services that are provided at schools, such as the salaries of school nurses, social workers, and speech therapists.

Both sides could negotiate over the remaining $300 million, according to the audit by the U.S. Department of Health and Human Services Inspector General.

But state officials replied in writing by saying they will contest the inspector general's findings. And the private firm hired to calculate the payment rates, Public Consulting Group, accused the watchdog agency of making numerous errors and suggested the federal government retract its report.

Disagreement is common between the state and federal bureaucracies that manage the massive Medicaid program, and negotiations can last for many months or longer. But the seldom has the amount in dispute ever amounted to so much money.

According to the audit, the state:

improperly included in its billings more than $400 million owed to the school employees' pension fund "despite not having made scheduled payments to the fund in nearly 20 years;"

incorrectly added the payroll costs of school employees who provided administrative rather than medical care;

did not submit records demonstrating how much time medical employees spent providing services.

Bryan Hawkom, a representative from the state's consultant, said it based the payment rates on a system approved by the U.S. Centers for Medicare and Medicaid Services in 2012.

The inspector general came "into the audit with the belief that the reimbursement rates were too high," and "the audit was performed to support this erroneous premise."

Hawks also disputed the statement that the state padded the bills by seeking payment for administrative employees, rather than nurses or therapists. "The activities are rendered by Medicaid allowable practitioners -- social workers," he wrote.

The consultant also rejected the finding that the state sought money for pension funding it never contributed. In 2003-04, when the rates were set, the state was paying 96 percent of its required contribution, he wrote.

After reviewing the state's and the consultant's replies, the inspector general said it stood by its report.

Susan K. Livio may be reached at slivio@njadvancemedia.com. Follow her on Twitter @SusanKLivio. Find NJ.com Politics on Facebook.