Samantha Davis, left, and Janelle Treibitz work at the Coalition for Nonprofit Housing and Economic Development on preparing for a rally and photo exhibit that centers on homelessness. (Matt McClain/The Washington Post)

The loss of affordable housing units in the District has caused a surge in the region’s homeless population, according to a new report that says single mothers and their children account for most of the increase.

Almost 12,000 people in the region were homeless Jan. 29, according to a Metropolitan Washington Council of Governments head count of people sleeping in the open or in shelters. Two-thirds of them were in the District, home to nearly all of the rise.

That’s about 400 more people, up 3.5 percent from the previous year. But the count might understate the extent of homelessness, because the winter’s extreme cold may have driven more people to double up with friends and family, COG says in the report, released Wednesday.

The nearly 7,750 homeless people counted in the District was 13 percent higher than the previous year, the report says.

Without the District, the region’s number of homeless people fell. Most jurisdictions recorded significant drops. The steepest, 39 percent, was in Arlington County. Loudoun County was the only other jurisdiction where there was an increase, but the relatively small number — 13 — was not considered statistically significant.

The District’s rise in homelessness is the flip side of its economic success. Its population has grown by more than 30,000 since the turn of the millennium, and the city is in the midst of a housing boom of apartments geared to the young and more affluent. And that has depleted the stock of low-rent housing for the poor and near-poor. During winter, emergency shelters were plunged into crisis, overflowing with an unprecedented number of homeless families.

There are 280 homeless families still in motels at the city’s expense, said Michael Ferrell, executive director of the D.C. Coalition for the Homeless. An additional 300 families are in an emergency shelter at the former D.C. General Hospital complex in Southeast Washington.

Ferrell said that almost half of the homeless families in the District are headed by a parent between the ages of 18 and 24. Most are single mothers with one or two children, he said.

When Phil Mendelson (D), the D.C. Council chairman who serves on the intergovernmental board, asked why the District’s number is rising while nearly everywhere else in the region it is falling, Ferrell said that the lack of affordable housing was the chief factor.

“More than 80 percent of homeless families are on public assistance with an income of less than $5,000,” he said. “They can’t afford any housing without a subsidy.”

Later, Mendelson said he remains troubled by the divergent trajectories of the District and the suburbs concerning homeless populations. The District guarantees residents the legal right to shelter when temperatures dip below freezing.

“I don’t know the reasons,” he said. “I wonder whether there’s something about the District that makes it more attractive for homeless to come. We need to understand why the District’s homeless population is growing when the rest of the region is dropping.”

In Arlington, where homelessness dropped 39 percent, County Board member J. Walter Tejada (D) said officials have made ending homelessness a priority and within a year expect to open a year-round shelter. Sharon Bulova (D), chairman of the Board of Supervisors in Fairfax County, where homelessness is down 21 percent since 2010, said the county had participated in programs that get homeless people into housing faster instead of languishing in shelters.

But the District also takes a similar approach, and it is not clear why the results are so dissimilar. One reason, Ferrell said, is that the District has a larger concentration of residents who are poor, while the suburbs have a bigger share of people who are affluent.

Peter Tatian, a researcher with the Urban Institute, said demand for affordable housing in the District has grown since the end of the recession, with the housing market gaining strength.

“Despite the fact we’ve had a lot of new construction and a lot of new housing units are starting to come online, it’s just keeping up with demand,” he said. “We still have people falling behind because their incomes simply don’t match what’s needed.”

Ed Lazere, executive director of the D.C. Fiscal Policy Institute, said the District’s homelessness is exacerbated by a national trend of well-paying jobs for college graduates but stagnant wages for workers lacking an education.

“We know at a time when the city is becoming more and more expensive, it’s getting harder to get a job to make ends meet for a large number of D.C. residents who don’t have a college degree,” he said.

COG’s report isn’t totally bleak: It says that more than 12,000 people are now considered formerly homeless because they have been moved to housing under programs designed to provide services and support to the chronically homeless as well as to those facing short-term economic crises.

“That’s one of the prime reasons why we have not had a significant increase in homelessness since 2010,” Ferrell said.

But the report cautions that many more residents are on the verge of becoming homeless because of high housing costs and fewer affordable options.

“While not yet considered homeless, many households are believed to be ‘doubled up’ due to difficult economic conditions,” the report says. “Homelessness is often the next step for such households once the family members or friends who have been sheltering them can’t or no longer will do so.”

By some measures, the region is lagging behind the rest of the country. The number of people in homeless families rose 9 percent in the past year in the Washington region, and it’s up almost 18 percent since 2010. In contrast, family homelessness has declined 8 percent nationwide since 2010. The region would have echoed the national trend but for the jump in homeless families in the District and in Prince George’s and Loudoun counties.

The report says that many homeless people have jobs but don’t earn enough to afford the region’s rents. According to the report, one in five homeless single adults is employed, as is one in three of the homeless adults in families with children.

Lazere has urged the District to adopt policies that place affordable housing on equal footing with other basic public services.

“We need to think of public housing as being like public safety, education and health care,” he said. “It should be a major part of what government provides.”