The Defense Department wants to add as many as 1,612 employees to oversee and audit contracts next year even as it plans for a 5 percent cut in the U.S. military’s budget.

Spending on the workers would rise 14 percent, to $1.9 billion, in fiscal 2013, from $1.7 billion a year earlier, according to the Pentagon’s budget request. Staffs at two defense agencies that manage and audit contracts would increase 10 percent, to 17,226, during the same period.

The military has been trying to catch up with an audit backlog that worsened with the spending surge that followed the Sept. 11, 2001, attacks. Defense contractors support the funding increase because it is aimed at shrinking $400 billion in unaudited contractor bills, said Alan Chvotkin, executive vice president of the Arlington-based Professional Services Council, which represents about 330 vendors.

“There’s money on the table that companies are probably owed,” he said in an interview. “As companies look at an austere environment, they want to get every dollar they’re entitled to.”

The government also may benefit by recovering as much as $2.2 billion in overcharges, according to the Commission on Wartime Contracting, appointed by Congress to address contracting problems. More than $30 billion has been wasted or lost to fraud from contracts tied to the wars in Iraq and Afghanistan, the commission estimated.

The Defense Contract Audit Agency completed $19 billion in “incurred cost” audits — reviews of expenses submitted under cost-reimbursement contracts — in fiscal 2011, according to the agency. That’s a 44 percent drop from the previous year, when it audited $34 billion in expenses.

The audit agency is seeking $574 million next year, a 16 percent increase from $495 million in fiscal 2012. It expects to complete $175 billion of incurred-cost audits in fiscal 2013, Elizabeth Robbins, a Pentagon spokes­woman, said in an e-mail.

The bump in funding should allow the agency to improve audit quality and “fully address the hefty backlog” by 2014, John LaBombard, a spokesman for Sen. Claire McCaskill (D-Mo.), said in an e-mail. McCaskill chairs a subcommittee on contracting oversight.

The Defense Contract Management Agency would get an 11 percent increase to $1.3 billion in fiscal 2013. It would add 79 people to oversee contracting in Afghanistan, where the Pentagon expects $20 billion in awards next year.

The Defense Department is requesting a total budget of $613.9 billion for fiscal 2013, including $88.5 billion for the war in Afghanistan.

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