Schools will soon be able to apply for grants from a $2 billion fund to help pay for Wi-Fi networks in schools under a plan approved Friday by federal regulators.

The Federal Communications Commission voted to set aside funds for Wi-Fi services over the objections of some schools and teachers unions, which wanted the agency to do much more. The National PTA and teachers unions wanted the FCC to increase the size of the so-called E-Rate fund to help cover the costs of Internet access to more schools. Demand has grown as more schools have tried to improve their Internet access, but funding hasn’t kept pace, they noted.

“Because of what we do today, 10 million kids will be connected next year who otherwise wouldn’t. That’s something to be proud of,” FCC Chairman Tom Wheeler said Friday.

Although the agency is setting aside up to $2 billion for Wi-Fi networks to be spent over the next two years, it assumes — but doesn’t guarantee — funding for those networks in future years. It also didn’t propose increasing the size of the program, although it asked for comments on doing that. Wheeler said it would “be a mistake to simply add money to a program that was set in the 20th century,” but the agency should continue looking at broader funding issues.

“I hope that going forward we will have the courage to fix this,” Democratic FCC Commissioner Jessica Rosenworcel said, regarding the limited funding available for schools and libraries. “I hope going forward we will be bold. Because this is not just a matter of getting schools and libraries connected — it’s a matter of our global competitiveness.”

The FCC said the cost of the program would be covered by unused funds and administrative cost-cutting. After internal discussion, the agency decided to continue to prioritize requests for Internet access to schools over requests for Wi-Fi.

The E-Rate program is part of the Universal Service Fund, a government subsidy program funded by a monthly fee on phone bills. It is mostly used to help cover the costs of providing telecommunications services in rural areas. The fund was started in 1996 and has grown over the years, even though E-Rate funding was capped at $2.25 billion annually 16 years ago and hasn’t been adjusted for inflation.

In 1998, the program gave out $2.3 billion to fund schools and rural subsidies. Last year, spending topped $8 billion, with $2.2 billion spent on Internet connectivity to schools and libraries.

The Universal Service Fund has often been a target of conservatives, who have complained about its ballooning costs. The FCC’s two Republican commissioners voted against the plan.

Republican Commissioner Ajit Pai complained that the E-Rate overhaul hurts rural school districts because it still requires a lot of paperwork that poorer schools can’t afford to hire consultants to complete. The FCC “has forfeited this opportunity for real, bipartisan reform of the E-Rate program,” he said. “Real reform would have meaningfully simplified the application process. It would have ended the unfair treatment of small, rural schools and libraries.”

The proposal was originally intended to attract support on both sides of the aisle, since most people want to improve Internet access for kids in schools and libraries. But it quickly became divisive as education advocates and others began questioning some of the proposed changes –- such as criteria used for allocating funds.

Ultimately, the Wi-Fi proposal drew bipartisan criticism, with Republicans upset that the agency was considering increasing funding from the Universal Service Fund, and some Democrats, including influential senators who helped create the E-Rate program, complaining that the agency wasn’t doing enough.