All of the District’s public libraries would be open on Sundays under a plan making its way through the D.C. Council.

Championed by council member Jack Evans (D-Ward 2), the proposal would have libraries open seven days a week and until 9 most weeknights in what would be one of the most significant expansions of services since the library system was created in 1896.

The bill, which will be before the council on Tuesday, comes three years after budget cuts forced the library system to close all but the central library on Sundays.

By enshrining expanded library hours in law, the Evans bill would make it harder to decrease funding for the library system, which often finds itself among the easy targets of budget officials looking for things to cut.

Evans, who chairs the council’s finance committee and is known for voting against tax increases, said that ensuring longer hours — and the money to pay for them — should be an obvious priority. But the mayor’s office, whose discretion would be limited by the proposed law, has raised concerns about the change.

Council members voted unanimously in favor of the proposal at its first reading Dec. 4 and will vote a second time Tuesday. If approved, the bill will be sent to Mayor Vincent C. Gray (D) for consideration as he prepares his budget proposal for fiscal 2014.

The changes would cost the District $9 million to $11 million, depending on the city’s final budget and library staffing expenses, D.C. chief librarian Ginnie Cooper said. Most of the funds will be used to hire about 100 new full- and part-time employees.

If Gray does not allocate the funds, Evans said, the council will. “At the end of the day, are you willing to pay for it? I am,” Evans said. “I’m willing to take money from the schools, from the human services, from the police department, wherever it comes from, to pay for the libraries.”

Evans said libraries are vital to communities, something he learned while growing up in Nanticoke, Pa., where he said the library provided a place for exploration and learning.

“Libraries were one of the few places you could go to look at books and see the rest of the world,” Evans said. “National Geographic, encyclopedias, things of that nature. . . . They provide a window for lots of people who otherwise wouldn’t have that.”

That purpose is the same in the District today as it was in Pennsylvania in the 1950s, Evans said. “It will educate our children, and there’s no price tag you can put on that,” he said.

Evans has become a strong advocate of the D.C. Public Library in recent years, citing frustration he said he hears at community meetings. He said the money for the expanded hours will come from a city surplus. But mayoral spokesman Pedro Ribeiro said it’s too early to tell. Gray’s office will work with the council to find funding based on 2014 revenue estimates and the outcome of Congress’s “fiscal cliff” negotiations.

“Maybe Jack has made up his mind that he knows where he’s going to go find the money, and that’s well and good in his mind, but that’s not how we operate,” Ribeiro said. “There are a lot of pieces that we need to know where they’re going to go before we start pulling money from specific places. . . . Right now, we’re still in that process.”

The Martin Luther King Jr. Memorial Library is the only location open Sundays, and it was scheduled to end Sunday hours last year until a public outcry led to a last-minute reversal by the city. The District’s most populous neighboring jurisdictions provide more extensive library service on weekends — eight Fairfax County public libraries and seven of Montgomery County’s biggest libraries are open Sundays.

D.C. library use has increased by nearly 10 percent since September 2011 — more than 3.3 million books, DVDs, audio books and other materials were checked out in fiscal 2012, according to the D.C. Public Library end-of-year report. In the same period, nearly half a million people attended activities including computer classes, meetings and library-run programs.

Additional hours mean greater opportunities for individual and community use, said Cooper, the chief librarian.

“Somebody who has a school assignment due on Monday will be able to go to the library on Sunday to get it done, should they leave it to the last minute,” Cooper said. “Forty percent of the time, an adult uses one of our public-access computers. . . . They’re doing it to check for availability of a job, polish a resume, make an application — since many of them have to be done online — and it’s our staff helping them to do that and our computers that make it possible for so many in the District.”

Expanded hours will also benefit workers who have only Sundays available to visit the library or bring children, said Alexander Padro, president of the Friends of the Watha T. Daniel/Shaw Neighborhood Library.

“We have some of the highest circulation and attendance at programs of any library in the city. Having an additional day to make those services available is going to make that performance even higher,” Padro said. “Whether you’re a child or whether you’re a senior, there’s something going on at that library every day that meets your needs.”

Neal Gregory, Friends of the Southeast Library president, said the Eastern Market branch, which has extended its hours while the Northeast branch is being renovated, enjoys heavy foot traffic beginning at 9:30 a.m. each day. Sunday was one of the branch’s busiest days before 2009 and probably would be again if the legislation passes, he said.

“The more hours that it’s available, the better, and the public can know that it’s available,” Gregory said. “It’s very confusing for a lot of people who don’t know if the library is open on a certain day or not. The idea of uniformity and the convenience . . . it’d be a nice service to the community.”