Fairfax County supervisor John C. Cook (R-Braddock)said this week that property-tax exemptions should be given to all nonprofits that offer social services in the county, not just those that provide affordable housing. The county’s Department of Tax Administration is studying what such tax breaks might cost.

“I’m a big believer in volunteerism. I also believe that our nonprofits are a key component for the work we do in the county,” Cook said in an interview Tuesday, a day after a Human Services Committee discussed the idea of possibly revising the criteria for exempting nonprofits from local property taxes. “If we’re going to really mean it — that we want to make nonprofits our partners with us — then we need to be helping them, not hindering them.”

Cook estimated that creating new exemptions might cost as much as $1 million a year, based on discussions Tuesday that exempting only affordable housing providers could cost about $225,000 a year. He also suggested that it would not shift any burden to homeowners, but could perhaps lead to privatizing more governmental services.

“It may mean that we can provide a service to the public by supporting a nonprofit rather than through the government,” Cook said.

The discussions arose at Tuesday’s meeting about the impact of taxes on nonprofits such as NOVACO, a group that provides transitional dwellings to victims who become homeless because of domestic violence.

NOVACO is eligible for a grant to help purchase such dwellings, but the nonprofit is not sure it can take advantage of the grant, at least in part because it could have trouble paying the recurring expense of local property taxes, its president said.

Joan Golden, president of NOVACO’s board, said Wednesday that NOVACO is eligible to receive a HUD grant, which is administered locally by the county, that would provide $480,000 to buy three two-bedroom condominiums. “It’s still something we’re considering,” Golden said, adding that the tax issue is an important factor but not the only one in deciding whether the organization can take advantage of the grant.

Cook said it doesn’t make sense for the county government to encourage people to help the neediest by giving donations to nonprofits and then turn around and tax those same groups for the county’s general fund spending. Cook said the county used to provide such exemptions on a case-by-case basis until the system got out of hand. Few were interested in reviving discussion about new tax breaks as the county has struggled to close budget gaps during and after the recent recession.

Cook also said he was confident that the criteria for such tax breaks could be written in such a way that the county would be able to benefit youth recreational organizations, health clubs or traditional charities such as the Salvation Army while avoiding giving tax exemptions to political advocacy groups or other nonprofits that might create controversy, such as Planned Parenthood.