The Prince George’s County Council on Thursday unanimously approved a $2.7 billion spending plan that restores Sunday hours at three public libraries, offers a modest increase for public schools and maintains a $50 million economic development fund that County Executive Rushern L. Baker III (D) has made a centerpiece of his administration.

The budget, which will take effect July 1, avoids unpaid furloughs for the county’s 6,000 employees, a contentious issue that was being negotiated until a few days before Thursday’s council vote. Baker, who had avoided proposing furloughs in his first two years in office, recommended up to five days of unpaid leave for employees, including police and firefighters, when he unveiled his budget proposal in March.

County Council Chairman Andrea Harrison (D-Springdale) and other members of the nine-member panel opposed the proposal and made other cuts to account for the $7.8 million the furloughs would have saved.

The property tax rate will remain at 96 cents per $100 of assessed value, but some tax bills will be reduced because home values are down. Property taxes are capped by law in Prince George’s.

The median value of a house in Prince George’s is $312,800, said Tom Himler, a top Baker aide. With the homestead credit for owner-occupied homes, the property tax on a house assessed for that amount would be $2,717, he said.

The budget also allocates $18 million for pay raises for county employees, although the county is still negotiating with some unions.

As council members combed through Baker’s plan in recent months, members decided to boost funds for public safety, adding a 30-member class of firefighter recruits and stepping up funding for drug enforcement in the county prosecutor’s office.

The lawmakers also added about $400,000 to expand youth employment programs and $200,000 for government-sponsored efforts to market the county as a place to work, live and play.

The budget also funds Baker’s proposal for a $25 million lease-purchase of a new police headquarters, with the possibility of spending an additional $2 million the following year for renovations. The council is still examining the terms of the deal.

The council allocated nearly $1.7 billion for the county’s 204 public schools, an increase of about $23 million from current spending levels. The extra money was designated for teacher pay raises and efforts to improve high school academics, among other purposes.

But the council declined to fund a nearly $2 million request from the Board of Education to hire 15 new staff members, saying it would await the outcome of a planned audit of the school system that is expected to begin this year.

The school board chairman, Verjeana M. Jacobs (District 5), said she was disappointed by the council’s decision to deny funds for additional board staff.

“I think that action was ill advised, premature, and unfortunate,” she said. “We all keep talking about how important education is. . . . It is the heaviest lift with the least amount of support.”

The school system, she noted, has a $90 million surplus, much of it attributable to vacant positions and savings in other areas. “In most places, it means you properly managed the budget, but we are getting criticized for it.” The county government’s budget surplus is about $45 million.

The council made no changes to Baker’s signature $50 million economic development fund, which has spent only $2.4 million on loans and grants to lure and retain businesses and jobs. More spending is planned soon, said Himler, the Baker aide. The new budget allocates $11 million for the program, which is slated to continue for several years.

The county’s library system got a $2.5 million boost to restore Sunday hours at three libraries, most likely New Carrollton, Oxon Hill and South Bowie, and to buy more materials. Baker had proposed a cut to the system of about $820,000, but an intense lobbying effort by Friends of the Library groups, council members, and the union representing library employees changed the outcome.

While acknowledging that there are “still challenges in the budget,” Himler said there would be a reassessment in the summer after an early-retirement program is completed. He said that the county had hoped about 250 employees would apply for buyouts but that so far only about 175 had. The deadline is Friday.

Himler said the changes the council made to avoid the furloughs “were very small,” and he praised members for their collegiality as the plan was being negotiated in recent days. But he also cautioned that tough days are ahead for the county, which has seen limited revenue growth in recent years.

“For us, nothing is off the table,” he said.

Baker praised the council, despite disagreements over some issues. “I am pleased that the adopted budget preserved funding in our priorities, especially our investment in education, public safety, and economic development, ” he said in a statement.