Housing activists pushing Arlington County to build 1,500 new units of affordable housing on county-owned land said Tuesday that they do not plan to back off after the County Board said it will consider the idea along with other proposals in the coming year.

“We are not going away,” said Robert Buckman, one of the leaders of Virginians Organized for Interfaith Community Empowerment (VOICE), which collected 10,375 signatures in the past six months in support of its plan. “Priorities are nice, but without deadlines, nothing happens.”

VOICE wants the county to commit to building those new apartments over the next three to five years for families making less than $50,000 per year. It identified 10 possible county-owned sites that would be suitable for such construction.

The County Board, in a unanimous statement Tuesday, said it will instruct the county manager to identify three to five sites where affordable housing could be built in the next 10 years, but warned that “priorities . . . would be based on core governmental function needs and debt capacity.” It also promised that a long-running housing study, due to be completed in a year, will examine the idea of “public land for public good” as a strategy to create affordable housing.

At a meeting of the board, both sides praised the construction of the Arlington Mill development, built on county land by a nonprofit developer and attached to a community center. Demand there is so high that 3,600 people applied for 122 apartments. The development is scheduled to open after the first of the year.

The rising cost of housing and the problems that creates for people whose wages don’t rise as fast is not limited to Arlington. The city of Alexandria, for example, just authorized its first housing master plan Saturday, calling for developing or preserving 2,000 affordable housing units by 2025.

The Arlington activists, gathered outside after the meeting, greeted the board’s response with skepticism while praising what it has done so far.

“We want this to be a different kind of affordable housing,” said Rev. Linda Olson Peebles of the Unitarian Universalist Church of Arlington. Most affordable housing is priced so that a family of four with an income of up to $64,000 can handle the rent. The bigger need, activists said, is housing for families who make less than $50,000. Half of Arlington households bring in more than $104,000 per year, and half bring in less. One quarter of the population makes less than $60,000.

“We applaud [the County Board] for taking a step. The neediest 50 percent . . . are nurses, doctors, teachers, people who care for our children, who can’t afford to live here,” said Rev. Tuck Grinnell of St. Charles Catholic Church.

The group vowed to return in May when the board works on its capital improvement budget and in November, when they want a developer to be named. The board warned that it could take longer; after the sites are identified in May, each one would have to go through Arlington’s land use review process and public involvement.