TAMPA — Families who rely on housing vouchers may have a chance at moving to neighborhoods with better schools and homes under a new federal rule that took effect this month.

But the rule may also saddle thousands of low-income families with higher rents if they stay put, local housing agencies warn.

Tampa Bay is among 24 metropolitan areas where housing subsidies will be raised in some neighborhoods so families can move out of high-poverty neighborhoods. But the flip side is lower housing subsidies in poorer neighborhoods that traditionally supply most of the region's Section 8 housing.

Local housing authorities say this has left them in a bind. They either make low-income families pay the shortfall or pass it on to landlords and risk losing them from the voucher program.

A Tampa Housing Authority analysis found that as many as 4,500 families in Hillsborough County could end up paying more in rent under the new rule. In St. Petersburg, Housing Authority leaders say they would need an extra $4 million per year to spare families from higher rents.

But the U.S. Department of Housing and Urban Development, which funds Section 8, is not providing any additional money.

"It's just an unfortunate situation; we've been told we have to put them in," said Tony Love, chief executive of the St. Petersburg Housing Authority.

Love's agency has requested a waiver to delay the new rule but it's unclear if HUD has any leeway.

HUD Secretary Ben Carson last year ordered a two-year delay for the rule, adopted under President Barack Obama's administration and known as Small Area Fair Market Rent or SAFMR. Local housing agencies needed more time to prepare, HUD said.

But after a civil rights group sued, a court ruled that HUD must move ahead with the policy.

While local housing agencies are concerned, some affordable housing advocates welcome the policy. They say it will help desegregate metropolitan areas and end the clustering of subsidized housing in certain neighborhoods.

More than 2 million Americans get subsidized housing through the Housing Choice Voucher Program, more commonly known as Section 8. Typically, it pays two-thirds of the cost of rent and utilities for low-income families. But under the old payment rule, vouchers were capped at a percentage of the average rent for an entire county or region.

In Tampa Bay, for example, a two-bedroom voucher would cover up to $1,045 per month for rent and utilities. As a result, families are often priced out of better neighborhoods where rents are higher.

Now, housing agencies must establish different subsidy levels for each ZIP code they serve.

For example, in downtown Tampa or Tierra Verde, where rents are among the region's highest, that same two-bedroom voucher would now pay up to $1,570, according to HUD data.

"It makes it easier for people to move out of low-rent areas, which are generally areas of racial concentration and low poverty," said Ed Gramlich, a senior adviser with the National Low Income Housing Coalition, a Washington, D.C., non-profit that advocates for more and better affordable housing.

If subsidies are reduced in low-income neighborhoods, the shortfall should be passed on to landlords, Gramlich said.

"Landlords are not keeping up properties and are getting more than they need," he said.

But local housing agencies fear that in a tight rental market, more landlords will refuse to take vouchers, reducing the region's affordable housing stock. And landlords in higher-rent communities may resist the "stigma" of subsidized housing because it could upset current tenants.

"The market is saturated with renters," said Margaret Jones, the Tampa Housing Authority's director of assisted housing. "Landlords don't have to deal with Section 8 if they don't want to."

In St. Petersburg, housing subsidies would drop in roughly nine of the 28 ZIP codes, according to officials there.

In 33709, an area that includes Kenneth City, the maximum subsidy would drop to $960.

The new rule does include a hold-harmless provision for tenants in existing leases but that would end once they move. And without additional funding, the higher subsidies in other ZIP codes could drain Section 8 funds faster, meaning fewer families can get assistance, officials said.

The SAFMR rule has already been tried in a handful of metropolitan areas with mixed results.

The city of Dallas adopted it in 2011. Among voucher holders who moved to different ZIP codes, those landing in so-called "high-opportunity" neighborhoods tripled, from 5 percent to 15 percent, according to the Center on Budget and Policy Priorities.

But in five metropolitan areas that adopted the approach more recently, the number of homes available to voucher holders in low-rent neighborhoods fell, a HUD study found.

Still, the study also found that more voucher holders in the five areas moved to higher-rent communities.

In the Sarasota-Bradenton metropolitan area, also required to adopt the new rule, subsidies in 40 percent of ZIP codes will decrease by more than $200 per month, said William Russell, president and chief executive of the Sarasota Housing Authority. They will rise in only 25 percent of ZIP codes.

Russell fears the result will be less choice for residents.

"At a time when we could least afford it, it will contract the available supply for our families," he said. "I think we're going to have a problem."

Contact Christopher O'Donnell at codonnell@tampabay.com or (813) 226-3446. Follow @codonnell_Times