Mayor Vincent C. Gray knows the number, precisely.

“Three thousand, nine hundred and sixty-four,” he ticks off, on a Saturday morning as he tours a Southeast elementary school. “I check the numbers daily.”

That would be the number of D.C. residents his administration has helped find jobs. It’s the yardstick by which Gray is measuring himself as he endeavors to make good on the cornerstone promise of his 2010 election campaign.

“This lack of jobs in the District is a ticking time bomb that affects us all,” said one piece of campaign literature.

Since being elected, Gray (D) has overhauled the city’s employment services department and rolled out a mix of long- and short-term initiatives aimed at getting residents to work in a city that spent more than 21 / 2 years with unemployment at more than 10 percent.

It’s hard to quantify how Gray’s efforts have made a difference, but the citywide unemployment rate stands at 8.9 percent, the lowest level in three years and only 0.6 points above the national rate. Compared with a year ago, there are about 18,400 more employed city residents, according to District statistics.

Gray said he is gratified by the progress. “I also recognize we have some distance to travel,” he quickly added.

The District has grown its job base, adding 6,600 jobs in the past year, according to figures from the city’s chief financial officer. But fewer than one in three of the city’s 736,000 jobs are held by a city resident.

City statistics still peg unemployment in Ward 8 as exceeding 20 percent. Neighboring Ward 7, the other ward east of the Anacostia River, stands at 15 percent. Those wards also voted most heavily for Gray in 2010.

In Ward 3, the city’s most affluent, unemployment is 2.3 percent.

“It’s the disparities,” said Martha Ross, a Brookings Institution fellow who has studied the city’s programs for the unemployed. “Parts of the city are doing pretty well and parts are still really, really struggling. . . . The city looks pretty good compared to other cities on a lot of markers about job growth and in some neighborhoods, that’s just not the case.”

The improving numbers, she added, are “really good signs, but they’re fragile.”

These days, ask Gray about his proudest accomplishments and he will note the dip in unemployment in those most troubled areas. Ward 8 is down to 22.5 percent, from 26.3 percent unemployment a year ago. In that same period, Ward 7 has gone from 17.8 percent joblessness to 15 percent, while Ward 5 has improved from 14.6 percent to 12.2.

Promises of jobs and economic development can be among the hardest for a government executive to deliver on. With city budgets tight, stimulative spending is not in the mayoral toolbox, and it’s up to Gray to beg, beseech and cajole private employers into hiring city residents.

The Gray administration’s marquee jobs initiative is called One City, One Hire — modeled after a Atlanta program that urged private employers to make at least one new hire a year. In the District, the challenge is less about getting companies to hire than getting them to hire city residents over suburban dwellers.

Part of the pitch, said Lisa M. Mallory, the District’s director of employment services, is to tell employers the city can offer a pre-screened list of candidates — taking the burden off the corporate human resources departments.

Where companies once complained about a lack of qualified candidates living in the city, Mallory said, “That’s not a viable excuse anymore.”

Lime Fresh Mexican Grill, a new restaurant in Columbia Heights, hired 30 city residents through One City, One Hire out of 44 new employees.

“Almost immediately, [city officials] came to me and said we have a lot to offer you to help,” said Mike Hedrick, a regional manager for the Florida-based chain. “They vetted all of the candidates for me, did pre-screening, looked at some of their résumés. . . . The candidates they gave me were good candidates.”

Hedrick said the process was “seamless” compared with other places where he has opened restaurants. “I’ve hired in other states where someone put up a notice on their Web site or their bulletin board, and I just didn’t get candidates, or I got candidates that were not a great fit.”

Still, Ross said it is unclear what effect One City, One Hire has had on the unemployment rate. But she has been pleased to see Gray tackle longer-term issues — improving coordination among employers, educators and city officials; focusing resources on the city’s new community college; and strengthening career education in public high schools.

“The Workforce Investment Council, for the first time, as far as I can tell, in 10 years, it is fully staffed,” Ross said, referring to a group that helps coordinate workforce training needs. “All of these are kind of unsung bureaucratic things, but they build a strong system.”

But Gray is counting on the short-term punch of One City, One Hire to deliver results for a mayoral term otherwise blemished by political scandal. As a part of the program, the city has organized “hiring events,” inviting pre-screened job seekers to apply for certain positions.

“It’s not one of those y’all-come cattle calls,” Mallory said. “We have employers, they give us their position descriptions, we talk with their HR folks, we say, ‘Exactly what do you need?’ And then we go out and find folks who meet all those requirements.”

Late last month, the city invited 250 residents to an event focused on hospitality jobs, featuring such employers as Hyatt, Omni hotels, the Washington Nationals and Ben’s Chili Bowl. Ahead of the interviews, applicants heard a pep talk from Gray, and went to seminars on providing good customer service and presenting a professional image.

Some of the applicants were skeptical. “There aren’t enough people from various organizations that are hiring people on the spot,” said Gregory Woodland, 61, before an interview with Omni. He had been looking for work since April, when he lost a cafeteria job at the National Zoo.

But many of those who showed up at the Walter E. Washington Convention Center said they appreciated the opportunity to have a one-on-one interview with employers — something not typically offered at job fairs.

Dennis E. Greene, 45, who lost a job earlier in the summer doing customer relations work with D.C. United, said it meant a lot to walk into a room knowing at least some of those out of work would get jobs.

“If 100 of us are in here and 10 leave with a job, it inspires the others to keep going,” Greene said. “A chance for a job beats no job.”

Greene — smiling, garrulous and sporting a truncated necktie — ended up getting more than a chance. During an interview, he connected with a Nationals rep over a mutual acquaintance. He walked out with a job offer.