The District government’s biggest program for easing a dire shortage of affordable housing is so poorly managed that millions of dollars in loan repayments have likely gone uncollected from developers while many low-cost apartments in the program are occupied by tenants whose incomes have not been verified, the Office of the D.C. Auditor said Thursday.

The program, called the Housing Production Trust Fund, has disbursed about $700 million over the past 15 years to help developers create affordable housing at a time when gentrification has transformed the city, with an influx of affluent newcomers driving up housing costs in many neighborhoods and pricing out longtime residents.

In coping with a dearth of affordable housing, the city has done a poor job of managing the trust fund by failing to diligently collect loan repayments; neglecting to ensure that developers offer the prescribed mix of housing for people in various income ranges; and not carefully monitoring whether apartments in the program are rented at proper prices and that all tenants are income-eligible, the auditor’s office said in a report.

D.C. Mayor Muriel E. Bowser (D), who made the issue of affordable housing a centerpiece of her 2014 campaign, vowing to alleviate the shortage, said through a spokesman Thursday that “we are making tremendous progress” toward that goal.

As for the critical audit, the spokesman, Kevin Harris, said, “While there is more work to do, residents should be clear that under this administration, the fund continues to make great progress in creating more affordable housing options across all eight wards.”

The trust fund, which has taken in about $1 billion since 2001, is financed by city taxes and overseen by the D.C. Department of Housing and Community Development, which lends money to developers to build or preserve affordable apartments and houses.

Although the city housing department said that 9,588 units of affordable housing have been created in 158 multifamily projects with help from the trust fund, the auditors said that after reviewing the department’s “unreliable” records for the fund, “we are not confident in the accuracy of the total number of projects or units.”

At a news conference Thursday, D.C. Council member Anita Bonds (D-At Large), chairwoman of the housing committee, said “the mechanisms needed for monitoring” the fund are “either grossly inadequate or simply nonexistent” at the housing department.

“Our inability as a government to effectively manage this essential tool means we’re failing to really do our part in addressing the affordability crisis,” Bonds said.

The audit was requested by D.C. Council member Jack Evans (D-Ward 2), chairman of the finance committee, who said Thursday: “This is not a criticism of those who have worked on [the fund] going back to 2001. This is an observation of how we can do it better.”

In preparing a report that calls for “significant improvements in the management” of the fund, the auditors said they visited diverse parts of the city and did in-depth examinations of 14 residential projects that include units of affordable housing financed by trust-fund loans to nonprofit and for-profit developers. Harris said 13 of the projects were financed by the trust fund before January 2015, when Bowser took office.

Polly Donaldson, director of the city’s housing department, said in a written response to the report that “an unrepresentative sample of . . . projects were selected for the audit review,” which skewed the results.

But she acknowledged that “there is always room for improvement” and said her department plans to sharpen its oversight of the trust fund by adopting the same strict monitoring procedures that are used to keep track of federal money.

The auditors said that the problems they catalogued at the 14 selected projects indicate that the trust-fund management failings are systemic, involving scores of affordable-housing projects citywide that relied on money from the fund.

In its lax oversight, the auditors said, Donaldson’s department also failed to demand annual financial statements from the developers or provide them with clear rules for how projects connected to the trust fund are supposed to be operated.

“While we found it encouraging that most property managers indicated that they wished to comply with legal requirements and wanted more guidance” from the housing department, the report said, “the agency appeared to have a hands-off approach to projects once they were selected for funding.”

In examining loan documents connected to the 14 selected projects, the auditors said, they tabulated $1.1 million in repayments that were delinquent on nine loans.

“Our sample is less than 10 percent of the approximately 158 multifamily projects that [the housing department] reported,” the auditors said. “The amount due for the entire [trust fund] portfolio is likely much greater and represents funds that could have been used for additional projects.”

Nearly 40 percent of households in the nation’s capital spend more than one-third of their incomes on housing, according to the city’s latest figures on poor families. More than 47,000 families are on the D.C. Housing Authority’s waiting list for public housing, and more than 7,500 people are homeless.

Tenants’ incomes are verified before they move into low-cost housing financed by the trust fund, the auditors said. The fund’s rules also state that developers who use money from the fund to create apartments have to annually recertify that their tenants are still eligible. But because the city never clearly specified how the recertifications should be done, developers have gone about the process haphazardly, the auditors said.

Some developers have not been checking each year on whether tenants’ incomes have increased, making them ineligible, according to the report. Other developers have come up with recertification procedures on their own — less-comprehensive than the process required by the trust fund — and then failed to follow those weaker procedures.

For example, at one of the 14 selected properties, the auditors examined a tenant’s bank statements and found income streams that made the renter ineligible for the apartment. This person had an online business that was bringing in $940 a month, the report says, “as well as other side jobs and PayPal transactions that totaled $6,159 in deposits over three months that were not included in that tenant’s certified income calculation.”

At another housing complex, “one tenant was certified at a salary of $55,000,” the report says. “Yet we found additional income of $5,000 when we reviewed bank statements that was not included in the certified income. This would have brought the tenant’s income to $60,000, over the [trust fund] limit for that unit.”

Without “a robust and consistent income recertification process,” the auditors said, the housing department “cannot ensure that the affordable units that the District invested in are actually filled” by income-eligible residents. “This means that households that do not meet the requirements are getting the benefit of the affordable units and lower rents, and, more importantly, those with a true need for housing assistance are not receiving it.”

The trust fund’s rules also state that 40 percent of disbursements each year must be used to create housing for families classified as “extremely low income,” meaning that their incomes are less than one-third of the local median income — $32,580 for a family of four.

Another 40 percent of disbursements must be dedicated to providing housing for families of “very low-income,” in the range of 31 percent to 50 percent of the area median. The rest of the disbursements from the fund must be used to create housing for “low-income” families, in the 51-to-80 percent range of the median.

But in 2014, the audit found, just 13 percent of the trust-fund disbursements were dedicated to “extremely low-income” families, only 19 percent to “very low-income” and 68 percent for “low income.” The 2015 disbursement percentages — the most recent figures available to the auditors — also were far out of balance, the report says.

It added: “The lack of compliance could have worsened the housing prospects for households who already have major challenges locating affordable housing.”