Facing pressure from City Council, the Kenney administration has agreed to a substantial change in its plans for Rebuild, a signature initiative expected to pump $500 million into the city's parks, recreation centers, and libraries.

In briefings with Council members Tuesday, the administration said it would allow smaller, neighborhood nonprofits to work as project managers on individual Rebuild sites, a role previously reserved for two of the city's larger nonprofits.

The project managers also will be selected through an open pre-qualification process. Council President Darrell L. Clarke had accused the administration of hand-picking partners without transparency.

The city also made a notable promise to district Council members, some who had voiced concern about having too little control — they get final say on which sites get refurbished.

"We've been hearing them and we're open to making adjustments, which we have," said David Gould, Rebuild's deputy director of community engagement and communications. "It's our hope that gets us to a place where everybody is more comfortable. We know we can't do this without Council."

The administration needs Council to approve funding for the project and on Thursday will introduce to the group three $100 million bond ordinances, to be issued at 24-month intervals.

Funds from the soda tax are to be used to pay down that debt. Gould said the administration would not issue the first bond until a lawsuit opposing the recently enacted tax is settled.

The rest of the funding is expected to come from philanthropic partners, grants, and existing city capital. The William Penn Foundation in November pledged to kick in up to $100 million.

Kenney has pitched Rebuild as a vehicle for broad economic and social change. Officials point to the jobs that will be created as facilities are improved or  rebuilt, then to those facilities' being community centers that will deliver essential services and strengthen neighborhoods.

Council members have expressed strong support for the goals. But the finer details have been subject to debate and criticism.

In a memo to his colleagues in December, Clarke slammed the city's plans to use as project managers only the Fairmount Park Conservancy and the Free Library Foundation. Project managers, after applying for and being approved to work on individual Rebuild sites, will be responsible for hiring and for overseeing the work.

Clarke pressed for a process that would bring in a diverse group of nonprofit partners.

Other Council members have expressed frustration about losing control of how money is spent at facilities in their districts, arguing that they know the communities best.

While the Kenney administration has taken steps to address those concerns — giving district Council members final say on Rebuild sites and opening the door to more nonprofit partners — it dug in its heels elsewhere.

Some on Council want Rebuild administered through the city's procurement and capital program office, rather than through outside nonprofits. That would increase the city's ability to handle large projects like Rebuild, supporters say.

Administration officials have said their way would be more effective and efficient while leveraging the nonprofits' ability to raise money. They have also said doing so would allow the city to avoid hiring through its low-bid system, opening the door to increased diversity.

The administration reiterated those points Tuesday.

Clarke's spokeswoman, Jane Roh, said he did not attend Tuesday briefings and could not comment on the administration's new proposal.

Councilwoman Maria Quiñones-Sánchez, whose district includes parts of North Philadelphia, said she was relieved to see the city move away from working with just two project managers but wanted to continue discussions about managing some of the projects through the city's internal systems, in hope of ramping up Rebuild more quickly.

"Progress," she said of the briefing, "but still missing a lot of details."

Councilwoman Jannie L. Blackwell, who represents West Philadelphia, said the same.

"This was the most detailed meeting," she said.  "But this is so very important and could involve so much funding that we're going to be involved, and want to be involved, from the beginning of the explanation until we understand all the details."