The former D.C. General Hospital now serves as a homeless shelter for many families. (Sarah L. Voisin/THE WASHINGTON POST)

D.C. Mayor Muriel E. Bowser is attempting to solve one of Washington’s most intractable social problems by increasing the number of homeless families given shelter by the government and broadening the conditions under which they can seek a place to stay at city expense.

On Tuesday, Bowser (D) announced that the District will accept shelter applications from families any day of the year, not just on freezing nights, as has been the policy for decades. Her staff said it had quietly begun testing the new policy and found a dramatic need: Almost 300 families have been given emergency placements in motel rooms since June.

The mayor said she will ask the D.C. Council to change a city law that requires homeless families to prove that they have nowhere else to go before they can get shelter. Instead, Bowser wants to offer families up to 12 days of housing while officials check whether they qualify for long-term help.

Bowser said she will also seek council approval of a plan to provide efficiencies, rather than apartments, for at least 250 homeless families — a cost-saving measure she said was key to fulfilling her campaign promise to close the city’s dilapidated family homeless shelter at the site of the shuttered D.C. General Hospital campus.

Taken together, the proposals provide the first blueprint for how Bowser plans to transform the District’s approach to its homeless crisis and accomplish her ambitious goal of ending chronic family homelessness in the city by 2017.

Advocates for the poor praised Bowser’s decision to allow year-round entry to family shelters but were deeply skeptical about other parts of the plan.

Amber W. Harding, a staff attorney for the Washington Legal Clinic for the Homeless, said the city should not lower the standard for housing for families. Legally, she said, the mayor’s proposal would eliminate any guidance on providing bathrooms, eating or bathing facilities, and defining family quarters as only four walls and a ceiling.

And she said protections need to be built into any law allowing an extended assessment period during days of temporary shelter so that families are not forced back into situations that in the families’ belief may not be safe.

“Forty percent of homeless families have suffered some type of domestic abuse,” Harding said. “We have to be sure that we’re listening to the families about what is safe or not.”

The mayor and her aides said they would establish a way for families to appeal rulings denying them long-term shelter. Bowser said it was her “great hope” that the new policies would help more families get back on their feet in an increasingly expensive city as well as lessen the influx of families into shelters after back-to-back years of record increases.

“Homelessness can seem so big and so insurmountable, but the fact is we can quantify the challenge,” Bowser said. “A city as prosperous as ours should and must solve the problem of homelessness.”

Bowser’s first move is to open the city’s long-term programs for homeless families to new applicants year-round. The District along with New York, Massachusetts and a county surrounding Minneapolis are among the few jurisdictions in the nation that make shelter a right for homeless individuals. But unlike in those areas, a 1980s-era rule in the District says that families can apply for shelter entry only on nights when there is a danger of hypothermia.

As a result, families that become homeless over the spring, summer and fall traditionally have had to wait until the first freezing nights of winter to enter a system that for most leads to subsidized apartments or other long-term shelter.

That practice has led to a flood of applications in early winter, creating a backlog of hundreds of families waiting at D.C. General and in motel rooms to be placed in transitional housing and matched with job training and other assistance. Last winter, 1,942 families applied for shelter and 1,007 were offered housing, city documents show.

Bowser’s administration has shrunk the backlog in recent months, moving more than 400 families into subsidized apartments and other transitional housing. But as it has for roughly two years, D.C. General remains at capacity, with almost 250 families, and an additional 350 families are in overflow motel rooms rented by the city. About 1,200 single adults are also utilizing nightly shelters paid for by the city.

Bowser’s predecessor, Vincent C. Gray (D), tried to restrict access to family homeless shelters in the belief that doing so would spur families to find better housing on their own. As a mayoral candidate, Bowser pledged to abandon that approach. She has vowed to end chronic homelessness in the District by 2020.

But the mayor said Tuesday that the city cannot afford to abide by a District law to build apartments to replace D.C. General. Instead, she said, she needs the council to give her flexibility to build 250 more modest replacement housing units: efficiency-style rooms, with some shared bathrooms and living quarters for multiple families.

The mayor offered no cost estimate for all of these proposals but said much of the expense could be covered by a 30 percent increase in the operating budget for homeless programs approved this year by the council. The council also gave Bowser $40 million to begin acquiring properties and building replacement shelters for the D.C. General site.

Bowser announced her plan before a meeting of the city’s Interagency Council on Homelessness, which voted on a plan to address this year’s expected influx of between 800 and 1,000 new homeless families.

Among other measures, the group approved expanding the definition of a hypothermic night. The District will now accept applications for shelter entry when the temperature falls below 40 degrees — instead of 32 degrees — as long as there is at least a 50 percent chance of precipitation.

Also, for the first time, the winter plan included data on hypothermic deaths in the city. Last winter, hypothermia was the cause of or a contributing factor in 10 deaths. But the study could not determine whether all 10 people were homeless.