On the first day of the District’s summer jobs program, Mayor Vincent C. Gray said the administration had found funding to hire about 4,000 more young people on a citywide waiting list.

The effort to add other employees marks a departure for the Gray administration, which aimed to rein in the troubled program’s costs and logistics by capping it this year for the first time, at 12,000 participants. On Monday, the mayor said he wanted to give a job to every eligible youth who signed up.

Gray cited revised revenue estimates for the current fiscal year — showing an additional $107.1 million in revenue, largely because of an improving economy — to justify expanding the program, which pays 14- to 21-year-olds minimum wage to work in government agencies and local businesses.

“There are some additional tax dollars,” Gray said. “I said the first priority is to get kids off the wait list.”

The extra revenue will help the city settle between $106 million to $125 million in spending pressures in this year’s budget, freeing up another $3 million to $5 million the city had saved (through a hiring freeze and other cuts) to spend on the summer jobs program, said Eric Goulet, the mayor’s budget director.

“Because some new revenue has come in, it allows us to free up the savings we were trying to generate and use them to eliminate the waiting list for summer youth employment,” Goulet said.

David Umansky, a spokesman for the District’s chief financial officer, confirmed that the mayor’s office is “reprogramming” existing funds to free up more money for the jobs program.

The expansion will bring the program’s budget above $20 million, harkening to recent years when the program swelled to more than 20,000 participants and cost more than $20 million. In 2008, youths were repeatedly sent to the wrong workplace, or weren’t paid, or were paid for doing little, if anything. More than 200 participants didn’t meet the city residency requirement, and the program ran $30 million over budget.

This year’s program was to be smaller, cheaper and improved. For the first time, applicants were asked to indicate their interests and employers were allowed to interview and screen applicants.

The first day of work on Monday appeared to run more smoothly than in recent years. Officials said only a few mix-ups were reported — such as participants arriving before their supervisors or requesting to be reassigned — but nothing unexpected.

The Department of Employment Services has a hotline to field calls, but the agency was mostly occupied with finding new placements for all the youths coming off the wait list. A department spokesman said the jobs would be found this week and participants would start July 5.

Mary Helen Thompson dropped her 20-year-old son, Matthew, off at Upshur Park in Petworth for his first day of work as a pool aide. Then she ran a few errands, and when she got home to 16th Street Heights, Matthew was there. He had showed up to work on time, at 8 a.m., but his supervisor was nowhere to be found.

Thompson called the program’s hotline, and was told the pool was closed Monday. The agency apologized for the mix-up and said Matthew should return at 10 a.m. Tuesday, also assuring Thompson that he would be paid for the day.

“I think they’re trying hard, but it’s obviously disappointing for someone on their first day,” Thompson said. “Hopefully, they’ll work out the kinks and we’ll go back tomorrow — at 10, not at 8!”

A 15-year-old was 10 minutes late to work at D.C. Central Kitchen, which makes meals for the city’s shelters and other organizations. Her supervisor told her if she was late again, she would be terminated. So the teenager said she planned to wake up at 5 a.m. on Tuesday and arrive by 7 a.m.

One of the eight students assigned to D.C. Central Kitchen didn’t show up, so supervisor Carolyn Parham said she was requesting a replacement, as well as a few more hands.

For a few minutes, the mayor filled in on Monday. Gray visited the kitchen around 1 p.m., donning a hairnet and chef’s jacket as he helped mix the meat sauce for the nachos — until he spilled tomato sauce on his white shirt, and left soon after.