D.C. Council members David Grosso, left, and Charles Allen listen as members discuss the “Homeless Shelter Replacement Act of 2016” during a city council meeting at the John A. Wilson Building on May 17, 2016, in the District. (Ricky Carioti/The Washington Post)

The D.C. Council unanimously backed publicly financed campaigns Tuesday, a move lauded by clean-government advocates in a city long plagued by its association with a pay-to-play culture.

Supporters say the program will open local politics to new candidates, increase the power of small donors and reduce the influence of deep-pocketed campaign contributors.

But critics — most notably Mayor Muriel E. Bowser (D) — say the program, estimated to cost D.C. taxpayers $5 million a year, will waste precious funds.

The voluntary system would allow qualified candidates to receive a base sum that varies by office, with a maximum of $160,000 for the mayoral contest as well as a 5-to-1 match on small donations.

If the D.C. Council approves the measure in a final vote expected next month, the District would join nearly 30 other jurisdictions — including Montgomery County, New York City and San Francisco — with a public finance system, according to Demos, a left-leaning think tank.

“In D.C., there is a real perception that residents aren’t the ones calling the shots — that it’s people with big money and developers deciding how development happens,” said Monica Kamen, co-director of the Fair Budget Coalition. “This is going to allow more diverse candidates to run, and it will mean candidates will spend time with their constituents rather than chasing wealthy donors.”

Bowser, who is accused by critics of being too closely linked with developers and other corporate donors, has said she would not fund the program.

But the council, which is responsible for approving the annual budget submitted by Bowser, can allocate money to pay for the program, said the bill’s author, D.C. Council member David Grosso (I-At Large).

A Washington Post poll last summer showed that District residents rated Bowser negatively concerning her efforts to curb the influence of wealthy political donors, with 48 percent saying she was doing a poor job while 31 percent said she was doing a good or excellent job.

Bowser spokeswoman LaToya Foster said the mayor believes that taxpayer dollars are better spent on the “many pressing needs” of residents, including hiring more police officers, investing in housing and fixing the city’s roads.

The mayor, who is running for a second term this year, has raised more than $1.4 million since announcing her reelection bid in late September, campaign finance records show. So far, she lacks prominent challengers. With the money Bowser has raised in just a few months, she is on track to meet or exceed her 2014 total of approximately $3.6 million in contributions.

Council member Charles Allen (D-Ward 6), who said he sometimes is asked about whether public dollars should be spent elsewhere, responds that there “is nothing more important than our democracy.”

“Yes, we absolutely have other funding needs, but I also believe the District can walk and chew gum at the same time, just like all the other jurisdictions,” said Allen, who chairs the council’s Judiciary Committee.

The cost of the program to taxpayers would vary by year, with the annual average around $5 million — a fraction of the city’s $13.8 billion budget. The earliest the program would be in place would be for the 2020 election cycle.

In Maryland, Montgomery County launched a public finance program for candidates this year, and in June, the Howard County Council approved its own public finance system, to begin in the 2022 election cycle.

For those who choose to opt into the District’s voluntary program, contributions to mayoral candidates and those running for attorney general and council chairman would be limited to $200. Individuals are currently limited to giving $2,000 in citywide races and $500 in ward races.

If a candidate participates in the public finance program, the maximum contribution would be matched with $1,000 from the city, for an effective donation of $1,200. Contributions to at-large council candidates would be limited to $100, and contributions to ward council candidates and at-large state Board of Education members would be limited to $50.

Contributions will be matched only if they are from District residents, although non-District residents may also make contributions subject to the limits.

To qualify for the matching program and the first half of the initial grant, candidates would be required to receive a specific level of support from D.C. residents, with mayoral candidates required to collect 1,000 contributions from D.C. residents totaling $40,000. To receive the second half of the grant, candidates would have to qualify for a listing on the ballot, which requires a nominating petition.

Council member Mary M. Cheh (D-Ward 3) said she supported the bill but wanted to make clear that there is work left to be done in addressing pay-to-play politics.

“We have to be realistic about what we’re doing today and what more may need to be done and not be caught in the romantic rhetoric of this bill,” she said. “This is not a bill that, of itself, addresses corruption. It will stand side by side with the conventional system of financing.”

Advocates, though, said it will be an important first step in engaging more District residents in politics.

Donors in local elections do not reflect city demographics, a 2016 report by Demos found.

White residents make up 37 percent of the District’s population but represented more than two-thirds of donors to D.C. Council candidates between 2012 and March 2016, the report said. And while just a quarter of District residents earn more than $100,000, residents in that income bracket represented more than 60 percent of campaign donors, according to the report.

Dexter Williams, who chairs the D.C. Fair Elections Coalition for Ward 7, said residents in his ward who have previously felt disillusioned by politics are excited about the public finance program.

“I’ve had candidates tell me that when they knock on doors, people tell them their donations don’t matter, but now their $5 will have an impact,” Williams said.