D.C. Mayor Muriel E. Bowser celebrated the first day of the city’s minimum-wage increase to $10.50 on Wednesday, calling the move an important step that “Congress has been unwilling to take” toward ensuring that citizens can survive in an era of rising costs and rapid local growth.

The increase is part of an incremental rise, signed into law in 2013, that will bring the District’s minimum wage to $11.50 an hour at this time next year — a change that Bowser said puts more residents “on the pathway to the middle class in Washington, D.C.”

But even as Bowser (D) hailed the increase, labor-rights activists across town were pushing to send the wage to $15 an hour.

Under the new District law, increases in the minimum wage will be tied to inflation after the pay level reaches $11.50. Labor activists want to see the incremental raises continuing until per-hour pay hits $15 in 2020.

At a hearing of the D.C. Board of Elections on Wednesday, activists trying to turn their campaign for the $15 wage into a ballot referendum opposed local business leaders.

If the board determines that that initiative merits a spot on the ballot, advocates of the $15 wage will need to collect about 23,000 signatures to get the measure in front of voters.

The activists’ efforts, meanwhile, put Bowser in an uncomfortable position. She has cast herself as a champion of the poor — someone working hard to “close the gaps” in a city with growing income disparity and a rising homelessness crisis that has hit working families and the unemployed alike.

But on Wednesday, Bowser was circumspect when asked why a $15 wage might not be appropriate for the District.

Different “jurisdictions,” she said, have determined wages to suit their particular “context.”

Bowser also said that this year’s wage increase was the product of hard work by her and colleagues when she served on the D.C. Council “to make sure that if you put in a good, hard day’s work, that you have a fair shot to live well here in the District of Columbia.”

But proponents of a higher wage said $11.50 is not enough.

Testifying before the Board of Elections, Matthew Hanson, the campaign director for Working Families, an advocacy group, said the current D.C. minimum wage isn’t a living wage. To make enough at the hourly rate of $11.50, a minimum-wage earner “would have to work 137 hours a week, 52 weeks a year,” he said. “Unless we do something to address this growing imbalance, it will only get worse.”

San Francisco, Seattle and Los Angeles have passed $15 minimum wages, and a national movement to set a $15 minimum has been gaining momentum.

In the District, Bowser said, a big part of the minimum-wage discussion last year involved this question: “What are the surrounding jurisdictions able to do?” Although Virginia was unwilling to raise its minimum wage in tandem with the District’s, Montgomery and Prince George’s counties in Maryland did.

“So we think that that continues to have us in a competitive place, because we want to continue to be a place where businesses locate,” Bowser said.

Additional strain on businesses was the focus of a survey released by the D.C. Chamber of Commerce on Tuesday. The chamber found that of the hundreds of local business owners it questioned, about half said they would need to reduce employees’ hours if the minimum wage rose to $15.

Most businesses, the survey concluded, also would not be able to hire additional workers.

In 2013, the District’s minimum wage was $8.25. Raising it to $15 by 2020 would mean nearly doubling wage costs for businesses in a relatively short period, the chamber said. Such a move also would put the District’s minimum wage at more than twice the current federal rate.

“This could make the difference in their operations and essentially in keeping the lights on,” Harry Wingo, president and chief executive of the chamber, said in a news release.“Increasing the cost of doing business in the District is the biggest threat to local companies, right on par with the recession, and will result in the [loss] of jobs.”

As $15-per-hour advocates and opponents testified before the Board of Elections on Wednesday, one board member wondered whether putting such a measure on the ballot would infringe on the role of the D.C. Council.

“Setting a minimum wage is a big deal,” said Stephen I. Danzansky, who argued that the measure being proposed was not unlike setting a budget or passing a law.