Counselors at one of the city’s largest shelters for homeless youths have had to turn away more than 80 unaccompanied children — some as young as 12 or 13 — who came to them for help in the past six weeks after the city cut more than $700,000 from the shelter’s budget.

Even as the number of homeless youths in the area continues to rise, the shelter had to turn away three to four teens a day since the city cut homeless prevention and family counseling grants this year, said Deborah Shore, executive director of Sasha Bruce Youthwork in Northeast Washington. The ­total amounts to about 7 percent of its $9 million annual budget.

Other nonprofit agencies that help the area’s homeless youths, including Covenant House and the Latin American Youth Center, have seen about an 18 percent decline in city funding this year, advocates said. This is a particularly challenging time, because many are also grappling with cuts from the federal sequester.

Doxie McCoy, a spokeswoman for Mayor Vincent C. Gray (D), said that the money was not being cut but rather “repurposed” to better serve the population of homeless youths in the District. There are more than 3,300 homeless youths in the District’s traditional public schools and charter schools, according to the D.C. Office of the State Superintendent of Education.

“We’re looking at services and we’re looking at agencies and . . . the issue is being attacked through a variety of services,” McCoy said.

The cuts come when the city is flush with cash in its reserves, and local housing advocates have been urging the mayor to do more to help disadvantaged residents, many of whom have been squeezed out of their homes in recent years because of gentrification. This past winter, the city’s main shelter for homeless families, on the old D.C. General campus, was filled to capacity, with more than 200 families, including nearly 600 children.

McCoy said the city Department of Human Services spends a little more than $3 million annually on youth homeless services, plus an additional $2.4 million this fiscal year just for “unaccompanied” youths, meaning children not under a parent’s care.

On Thursday, McCoy and Shore presented conflicting accounts of why the funding for Sasha Bruce evaporated.

McCoy said about $130,000 would be redirected to a Department of Human Services program for counseling and support for families dealing with adolescent conflict.

A $430,000 grant to Sasha Bruce from the city’s Department of Youth and Rehabilitation Services was renegotiated to include emergency beds only for court-detained youths, not homeless ones, Shore said. “They have clearly made a decision to make choices that leave out runaway and homeless youth,” she said.

Other nonprofit groups that help homeless youths have lost funding recently.

Lori Kaplan, the president and chief executive of the Latin American Youth Center in Columbia Heights, which works with about 4,400 young people from the District and Maryland each year, said that the loss of $220,000 in city funds means that the center will have to turn up to six young people out of transitional living quarters. The center houses 40 to 50 youths a year in its emergency-shelter and transitional housing programs.

“We’ve been trying to get the city to put more funding into the homeless, but the impact of all our advocacy sadly has been cuts, not increases,” Kaplan said.

For workers on the ground, the effect of lost — or redirected — money has been clear and immediate. One counselor at Sasha Bruce House recalled trying to counsel a sobbing teen seeking a place to sleep after her mother lost the family apartment, and being able to do little to help.

“To not be able to help somebody and know there is not any other option for them — it’s heartbreaking, it’s awful,” said Gina Bulett, the primary counselor. The program now just has five emergency beds, down from 16 last year, but houses dozens more in apartments.

Many young people are bunking with friends or relatives, sleeping in their cars, or living in laundromats, Bulett said.

Vernon Perry, 20, became homeless two years ago while he was a senior at Ballou High School in Southeast. He and his mother lost their two-bedroom apartment after she could no longer afford the rising rent.

The two spent months couch-surfing from place to place, bunking with friends and relatives. Perry dropped out of school and ended up sleeping in his car on some nights. A flier for a GED program led him to Sasha Bruce, where counselors helped him get a place in a small apartment.

The first thing he did when he entered his new home was dive into his bed and fall asleep, relieved to be in a stable place.

“I know a lot of people in my situation now, going through the same thing I went through, nowhere to go at night,” he said. “You’ve got to have stability.”