Supporters of the "living wage" bill gathered in front of the Wilson Building last month. (Jared Soares/For The Washington Post)

While District leaders spent much of the year debating and ultimately rejecting a “living wage” for retail employees in the city, the D.C. government was failing to comply with a law requiring it to pay a similar living wage to its own contractors.

The Living Wage Act passed by the D.C. Council generally requires companies working under city contracts of $100,000 or more to pay employees wages that are reset every year based on ­cost-of-living estimates.

In 2010, the wage was set at $12.50, but it hasn’t been updated under Mayor Vincent C. Gray’s tenure. Worker advocates who have been pressing the Gray administration for an update say the lack of action has cost low-wage workers thousands of dollars.

If it had been updated as required, the wage would now stand at $13.40, according to the city.

Ari Weisbard, deputy director of the Employment Justice Center, estimates that a contract employee who is working standard hours while making the current legal minimum of $12.50 an hour has missed out on more than $3,000 in pay since 2011, when the wage was due for an update.

“That could be two months of rent or several months of grocery bills they are falling behind on,” Weisbard said. “It makes a huge difference to these workers to lose that amount of salary.”

The city agency in charge of the rate recalculation, which is based on the cost of living in the region, has acknowledged the need for a recalculation of the minimum wage.

In March, the Department of Employment Services told the D.C. Council that it was “preparing to calculate and review the rate.” Last week, department spokeswoman Najla Haywood said that agency director Lisa M. Mallory and other mayoral officials “are working to prepare a recommendation to [Gray], who will act on it shortly.”

The questions about the wages paid to the city’s own workers comes as government leaders continue to debate how much workers generally should be paid in the District.

Legislation that would have required large retailers, including Wal-Mart, to pay their employees wages and benefits of $12.50 an hour died after the council failed to override a veto from Gray (D). Now attention has turned to an across-the-board minimum wage increase, with five competing bills introduced by council members and Gray offering tentative support for such a move.

Administration officials fam­iliar with the matter but not authorized to speak publicly say the delay in updating the living-wage rate for government contracts is wrapped up in a policy dispute over whether the living wage should apply to contract workers caring for the mentally ill or developmentally disabled who are paid using federal Medicaid funds.

In the spring, Mallory sent a memorandum to Gray’s policy director asking for a determination on whether the living-wage law should apply to group home workers and home health aides, citing concerns from several ­other city agencies. But there has been no decision.

The memo also included draft calculations of how the living-wage rate should have been raised in previous years. The $12.50 wage in 2010 should have been raised 20 cents in 2011, another 40 cents the next year and, finally, to $13.40 today, according to those figures.

At least some group home workers are not making the 2010 living-wage rate.

Ray Hamlet, 53, worked as a counselor last year in a Southeast Washington group home for the mentally disabled, often working 50 hours or more a week. He said he made $11.75 an hour, and he is battling his former employer for overtime wages he says he is owed.

Hamlet said he made more than $13 an hour in other group home jobs. None of those jobs, he said, included benefits such as health insurance.

“It’s a problem,” he said. “Anytime you’re working with disabled people, you should be making more than $11.75.”

If the city revises the living-wage rate, it is unclear whether workers would be paid retroactively for time worked since the first increase should have been issued in January 2011. And if retroactive raises are authorized, it is unclear whether contractors will have to bear that cost or whether the city would be on the hook, potentially for millions of dollars in back pay.

Weisbard noted that the last time the city updated the living-wage rate, in July 2010, it made the increase retroactive to Jan. 1, when the increase was due under the law. “Some level of retroactivity is really the least we can do,” he said.

Pedro Ribeiro, a Gray spokesman, said the mayor has “always been committed” to paying city workers fair wages. He pointed to Gray’s move this year to conclude new contracts with city employee unions guaranteeing pay raises totaling 13 percent over four years for roughly two-thirds of the District workforce.

“I think his track record is established on that matter,” Ribeiro said.