Mayor Vincent C. Gray will ask the D.C. Council for emergency power to decide whether homeless families seeking shelter on freezing nights have no other place to stay.

The measure is intended to stanch the flow of record numbers of families into taxpayer-funded shelters this winter.

Gray’s move comes in response to an unprecedented 135 percent increase in families entering D.C. shelters since the fall. The mayor’s aides have labeled the increase a “crisis,” and it has become an issue in the city’s April 1 Democratic primary, with Gray’s challengers contending that the number calls his leadership into question.

Gray (D) has said that keeping people from entering shelters or moving them into other types of temporary housing is the best way to push families toward self-sufficiency.

In the most heated exchange of any mayoral debate, Gray recently said the council was to blame for this year’s homeless surge because it rebuffed a similar request last year. By proposing legislation to the council, Gray will throw the issue back to his four leading challengers before the primary, forcing them to consider a possible means of easing the homeless crisis.

A draft of Gray’s proposal, obtained by The Washington Post, would fundamentally alter a District law that grants any resident a “right to shelter” on nights when the temperature drops below freezing and the city declares a hypothermia alert.

Council Chairman Phil Mendelson (D) said it would be up to the council to find the right balance between protecting homeless families and giving the administration the tools needed to reduce the shelter population.

Under Gray’s plan, families would be given shelter on a provisional basis, but caseworkers would immediately begin to determine whether they have other housing prospects, including sleeping on the couches or floors of relatives or friends. The city would have to make a decision within 14 days.

Those who have such options would be required to leave city-funded rooms within 24 hours, even if the temperature remains below freezing.

“Our goal is to get people out of shelters . . . or never into shelters in the first place, even if that means living with a grandmother, a sister, whatever,” said Chris Murphy, Gray’s chief of staff. “If someone is doubled up in a safe situation that is determined to be appropriate, we think that is acceptable. Families have done it for generations. Immigrant families do it. It’s not an unacceptable situation.”

The District is one of a handful of jurisdictions in the country that says residents have a right to shelter on cold nights. Once sheltered, families may stay until the city has helped them find permanent housing that they accept. New York City and Massachusetts have similar laws.

With the onset of freezing nights, scores of families usually enter the city’s homeless shelter at the former D.C. General Hospital campus, and they stay for weeks or months. During the first freeze this past fall, however, that shelter was still full from the previous winter, and the city began renting motel rooms for families that said they had nowhere else to stay.

Gray’s aides said they believe that the motel rooms provide a more attractive option for families doubled up in crowded housing arrangements: Parents who might have steered clear of D.C. General — with its unreliable hot water and occasional bed bug infestations — decided that a taxpayer-funded motel room was a good option for their children.

The District now has nearly 300 families in the former hospital and more than 400 in overflow motel rooms in the District and Maryland. Officials have estimated that hundreds of families could continue to languish in shelters and motels until spring 2015 — at an annual cost of tens of millions of dollars.

“We do not believe that there is a family homeless crisis that many people claim there is,” Murphy said. “We think there is a crisis of too many families in shelters, and that’s a meaningful distinction because it drives how you solve the problem.”

Gray’s plan includes limited measures to deal with the record number of families in shelter. For instance, Murphy said, the administration wants a citywide “call to action” that would ask landlords to volunteer apartments for a program in which the city pays homeless families’ first four months of rent.

Gray will ask for a vote on the emergency legislation at the council’s next meeting, March 4.

Patty Mullahy Fugere, executive director of the Washington Legal Clinic for the Homeless, said Gray’s plan does not account for what happens when a family sent to live temporarily with friends or relatives exhausts that option.

“Is it okay for someone to be sent to stay with their godmother if their godmother can only take them for a week and nothing more?” she said. “If a family is diverted and then loses that placement through no fault of their own, they wouldn’t be able to come back to the shelter until the following winter during a hypothermia alert. They have no public safety net at that point.”