A pot of money that’s supposed to be dedicated to a broad strategy for New Orleans housing but traditionally has been used for less comprehensive line items in the city budget could be rededicated to an updated version of its original purpose under a proposal approved this week by a City Council committee.

Mayor Mitch Landrieu’s administration, however, says a change could undermine blight reduction efforts and other city programs.

Councilwoman LaToya Cantrell, who is sponsoring the ordinance endorsed Wednesday by the Community Development Committee, said the plan to strengthen the rules for the Neighborhood Housing Improvement Fund would be a step toward providing a better approach to housing for low- and middle-income residents.

“We’ve needed a housing plan for a long time. We’re behind the eight ball, but we’re getting there,” she said.

The fund, which Cantrell said generates about $3 million a year, is supposed to be used according to a housing plan devised by an advisory committee, though that hasn’t occurred in recent years and the committee no longer exists. Instead, the money is typically just included as part of the general budget drawn up by the mayor and approved by the council.

“This is the council’s ordinance, and to date, we haven’t been following the law,” Cantrell said.

Her proposal would set up a new committee to oversee the fund; it would receive applications from programs hoping to use the money. The committee’s recommendations, which would be tied to both the city’s master plan and a more specific plan for housing, would then be passed on to the council for its approval.

There are no firm rules in the current ordinance on how the money can be used. Supporters, representing nonprofits and a developer, pitched a variety of specific ways they would use the money on Wednesday, including fixing blighted properties whose residents can’t afford repairs, helping to offset the cost of building affordable housing units and helping to close the gap between Road Home funding and the cost of rebuilding for residents still trying to return home.

That gap runs an average of $40,000 a family for those working with the Lower 9th Ward Homeownership Association, said M.A. Sheehan, the group’s housing director.

Cantrell also has proposed using the money to set up a revolving loan fund that would help residents buy or repair homes and then would be replenished as they paid it back.

Four council members supported the ordinance at Wednesday’s committee meeting. That could set up a fight with the Landrieu administration, which is, at best, cool to the idea.

Some of the money now goes toward providing the local match for a federal affordable-housing grant program, and some is spent on upgrading houses to accommodate residents with disabilities. That program upgraded 22 homes last year for about $591,300. About five have been completed so far this year, with another 30 in the pipeline.

A bit less than a third of the money goes toward paying staff in the city’s Code Enforcement Department, to deal with blight, and housing staff in the Law Department.

“As blight is a top concern among the city’s residents expressed at nearly every community meeting, we caution against any attempt to reduce funds critical to fighting blight without replacing them,” Landrieu spokesman Brad Howard said in an email. “To do so would hinder the city’s ability to reduce blight and get results for the public.”

Follow Jeff Adelson on Twitter, @jadelson.