Philadelphia is on the brink of becoming the first U.S. city to bar employers from asking potential hires for their salary history, a step aimed at narrowing the pay gap between men and women.

The wage-history bill unanimously passed by the city council now sits on the desk of Democratic Mayor Jim Kenney who said Thursday he expects to sign it as soon as Monday.

Key players in the business community, including Comcast Corp. , are pushing for a veto, claiming the ordinance, passed in December, wouldn’t work as intended and saying it would violate employers’ free speech rights.

But Mr. Kenney said the city doesn’t think the bill’s critics have valid legal arguments.

“We may get sued, we may not,” he told reporters Thursday. “But council passed this measure by a unanimous vote, and I see no reason why I shouldn’t sign it.”

Rob Wonderling, chief executive of the Chamber of Commerce for Greater Philadelphia, said the bill is the council’s latest antibusiness move, after passing mandatory paid sick leave and living-wage mandates in recent years. He said these measures create a pattern sending “a very negative signal that there is a significant hassle factor if you want to set up a business or conduct business in the city of Philadelphia.”

The dispute comes as advocates for progressive policies are increasingly turning to cities, where Democratic officeholders are more likely to back the proposals than in Congress or Republican-led state legislatures, said Brian Egan of the National League of Cities.

The National League of Cities says Philadelphia is the first U.S. city to pass a wage-history bill. It was also the first city to pass a measure taxing soda, which has subsequently been adopted elsewhere such as San Francisco and Cook County, Ill. Cities like Portland, Maine and Seattle have enacted fees or bans on plastic bags.

In Pennsylvania, women earn 79% as much as men, while black women make 68% as much as men, according to the city’s ordinance, citing a Census Bureau report from 2015.

Basing a worker’s pay on their previous wage “only serves to perpetuate gender wage inequalities,” the bill says, noting the gender wage gap hasn’t budged much since Congress passed the Equal Pay Act in 1963.

Last year, Massachusetts moved to prohibit employers from requiring job applicants to provide their salary history before receiving a formal job offer, as part of a broader pay-equity bill set to take effect next year. Republican Gov. Charlie Baker signed the bill despite opposition from business groups like the Associated Industries of Massachusetts.

Massachusetts was the first state to enact such a law, according to the National Conference of State Legislatures. California passed a similar measure last year that doesn’t bar wage-history inquiries but prohibits employers from using prior salary as a justification to pay employees different wages for similar work.

Some critics of the Philadelphia bill contend it wouldn’t withstand a court challenge, potentially putting the city on the hook for significant attorneys’ fees.

Comcast, headquartered in Center City, is the eleventh-largest private employer in Philadelphia, according to the Pennsylvania Department of Labor and Industry. The company says it has about 8,000 employees in the city. The education and health sectors account for 31% of local jobs, Bureau of Labor Statistics show. The University of Pennsylvania has the most workers.

“We believe that the strength of the likely legal challenges to the city’s speech-focused approach to remedying pay inequities due to sex discrimination makes a veto appropriate and necessary here,” Miguel Estrada, a lawyer with Gibson, Dunn and Crutcher, wrote in a letter to City Solicitor Sozi Tulante, on behalf of Comcast and other Chamber of Commerce members concerned about the bill.

The wage-history prohibition would restrict more speech than necessary to serve a “compelling” city interest, Mr. Estrada wrote in the letter. He said the bill is based on the assumption that “relying on previous wages necessarily perpetuates gender wage disparities based on sex discrimination.”

The city’s Chamber of Commerce proposes a different approach that would give “greater precision” to the Equal Pay Act by ensuring any pay differences were based on permissible factors, such as education, training or experience. That would help close the wage gap because over time it would “tend to isolate and wash out the effects of previous sex discrimination,” said Liz Ferry, the Chamber’s vice president for state legislative affairs.

Councilman William Greenlee, a Democrat, who sponsored the bill, says the measure wouldn’t prevent employers from setting a fair salary, bar salary negotiations with prospective hires, or keep job candidates from voluntarily sharing their pay history. But if passed, violators who quizzed would-be hires about salary could face fines up to $2,000.

Mr. Greenlee says he is surprised by continued efforts to derail the bill because no one testified against it at a public hearing. He thought amendments had largely satisfied concerns the Chamber of Commerce outlined in written comments. “They went from one extreme to another and are threatening lawsuits and all this kind of stuff,” he said.