Mayoral candidate Carol Schwartz speaks during the AARP D.C. Candidate Forum sponsored by AARP at Mount Vernon Place United Methodist Church in Washington on Oct. 9. (Sammy Dallal for the Washington Post)

Standing on a trash-strewn bank of the Anacostia River, D.C. mayoral hopeful Carol Schwartz announced Tuesday that she would devote a new cabinet-level office to closing the divide between poor neighborhoods on one side of the water and increasingly gentrified areas on the other.

Gesturing to the bridge that spans the river, the independent candidate promised to be a bridge herself between east and west. Empty coffee cups and plastic bottles littered the ground behind her feet. “We want to see the trash,” she told her volunteers as they set up “Carol for Mayor” signs. After all, the purpose of her news conference was to highlight some of the city’s uglier inequities.

“Washington, D.C., is a tale of two cities,” Schwartz declared, echoing a populist theme that propelled New York City Mayor Bill de Blasio into office and fueled the failed D.C. mayoral bid of Andy Shallal in the Democratic primary.

In one, there are amenities galore for those who can afford it; in the other, a mile away, there is barely a restaurant. “Ours has become a city that too often fuels its future at the expense of its distinct and rich diversity,” she said.

Rising housing costs, a growing homeless population and stagnating school achievement are some of the District’s deepest challenges — and among the issues most directly guiding voter ­choices in this year’s mayoral race.

Muriel Bowser may have raised the most money. But more potential voters, individuals who live in the District, gave to David A. Catania.

Schwartz, a resident of Northwest Washington, has made unease with the city’s gentrification in recent years a cornerstone of her campaign, hoping voters unnerved by the rapid changes they see will turn to a familiar face.

She solemnly read many statistics showing the wide gap between rich and poor in the District, noting that the richest 5 percent of Washingtonians make an average of $531,769 a year, while the bottom 20 percent earn an average of $9,900, and that unemployment in Ward 8 is about six times as high as in Ward 3. Obesity rates, smoking rates and HIV-related deaths are significantly higher in poorer parts of the city as well, while high school graduation rates are far lower.

To address such numbers, Schwartz proposed creating the Mayor’s Office of Disparity Solutions. The cabinet-level agency would involve a task force of representatives in and out of government focused on narrowing gaps between the city’s wards in education, health care, employment and technology.

Each government department would have a staff member devoted to disparity issues, she said, and the office would coordinate among them. For example, she suggested that a technology-based scavenger hunt like the one hosted by the D.C. government this year could include a health-care component. In-school training programs could encourage students to become police officers and firefighters. The office would also regulate and encourage informal, nonprofit lending circles as California has.

Along with the new office, Schwartz proposed a new government hotline and Web site, 111 and, devoted to listings for employment, internships, adult education and job training. She also pledged that as mayor, she would use tax credits more aggressively to attract primary-care providers and businesses east of the river.

“Bridging disparities will take a leader who is beholden only to the people of this city,” said Schwartz, who served four terms as a Republican on the D.C. Council. “I am that leader, and someone who built bridges my entire career.”

Disparity issues may have contributed to council member Muriel E. Bowser’s lackluster performance east of the river in the Democratic primary, when Mayor Vincent C. Gray earned broader support among working-class voters. Although Bowser edged out Gray overall, he led her in wards 7 and 8.

Looking at where key candidates stand on pressing issues facing Washington.

Since the primary, Bowser, who represents Ward 4 in Northwest Washington, has been working to shore up working-class support. She has pledged to create a new deputy mayor position to promote economic opportunity east of the Anacostia River, appoint a “workforce opportunity” adviser and expand the power of the District’s small business department.

She has faced competition on the topic from Schwartz and from fellow council member David A. Catania (I-At Large). Catania, who trails Bowser in recent polls, has focused on improving the struggling public schools as a means to close income and opportunity gaps across the District.

Schwartz did not offer a cost estimate for the new agency, saying it would not be a large bureaucracy but a coordinating body. “It’s all very just catch-as-catch-can” now, she said, something the new office would help correct.

“This will be a mayor’s —, ” Schwartz said, before catching herself. “This mayor. This mayor’s priority.”

The question of electability has dogged Schwartz throughout this race. At 70, she has four failed mayoral bids behind her. In polls and fundraising, she lags far behind Bowser and Catania.

“Certainly the other candidates have more money,” Schwartz said. But she questioned the legitimacy of a recent poll from a group called Economic Growth D.C. in which she drew just 12 percent. “The other polls have been showing me at 16 percent,” she said. “It’s less than the others, but we’ve still got a couple of weeks left.”

Schwartz acknowledged that she doesn’t have the money for TV or radio ads, unlike Bowser and Catania, but she said her enthusiastic volunteer network could help counteract that influence. “There's a huge amount of support out there,” she said. “They really recognize me.”