The District’s school system failed to fill its summer-school seats for students in kindergarten through eighth grade this year after officials implemented a new invitation-only admissions policy that triggered criticism — and an injection of additional funds — from the D.C. Council.

The invitation-only policy, part of a broad overhaul of K-8 summer school, was meant to target lagging readers who school officials believed would benefit most from the five-week program. But it left out some of the students who are furthest behind.

As the end of the school year approached, school officials realized that invited students would not fill the 2,700 available slots. Officials then opened the program to all K-8 students and as of late June had filled 90 percent of seats, with hundreds more on wait lists. But many students did not show up, and as of late July, only 1,827 were enrolled.

School system officials said they do not believe the shortfall is related to the new admissions policy because every year, significant numbers of students enroll in summer school and then fail to show up.

“We do our best to factor that in, but it is not at all related to our enrollment policies or our approach to prioritizing the students who could best be served by our summer programs,” said spokeswoman Melissa Salmanowitz. “We enrolled every student that was interested in summer school.”

The school system’s K-8 program represents its central summertime effort to change the trajectory of low-performing elementary and middle school students, including more than 10,000 struggling readers.

Meanwhile, a summer program for rising freshmen — part of a broader effort to improve ninth-grade performance — enrolled 1,244 students. An additional 1,549 students are in high school summer programs, and 2,800 children attend publicly funded camps run by community-based organizations. Still other students are attending summer programs run by individual schools.

Research has shown that children tend to lose academic ground during the languid summer months. The problem is especially acute for poor children, who often have less access to out-of-school enrichment than their more affluent peers.

Although the District’s did not meet its enrollment target, the program — once totally disconnected from school-year academics — has made important strides, Salmanowitz said.

“For the first time this year, we have a summer-school curriculum that aligns to the work the students do during the school year and meets the specific needs of students,” Salmanowitz said. “Based on the success we’ve seen with that model, we will work aggressively to serve more students in summer school going forward.”

In addition to tying summer learning to school-year expectations, officials required this year’s summer-school teachers to be rated effective or highly effective in order to work.

“They were handpicked. That makes a huge difference,” said Gladys Hetherington, a teacher who is serving as the principal at Brookland Education Campus, one of eight sites for the K-8 program across the city.

Another summer site, Bancroft Elementary School in Mount Pleasant, buzzed one recent morning with the same kind of routines and lessons that are common during the school year.

In one classroom, students sat at desks writing about characters in the novel they’d been reading together, the E.B. White classic “Charlotte’s Web.” In another, an aide taught a small-group lesson tailored to students’ particular struggles. In a computer lab, fifth-graders clicked away at software designed to reteach and reinforce math skills.

The program’s effectiveness won’t be formally evaluated until students take assessments when they return to school in the fall, but teachers have been monitoring progress throughout the summer. It appears that most students have maintained or improved their reading and math skills, said Kara Kuchemba, co-principal at the Bancroft site.

D.C. Council member David A. Catania (I-At Large) recently introduced a measure that would require summer school for students who are below grade level and at risk of not advancing to the next grade. He led the council’s push in May to allocate an additional $4 million to expand summer programs, half for the traditional school system and half for public charter schools.

Mayor Vincent C. Gray (D), who had planned to spend the money on affordable housing, opposed the move, arguing in a May 9 letter to D.C. Council Chairman Phil Mendelson (D) that “it is not clear that there is sufficient demand for or capacity to grow” the school system’s summer program. School officials said the $2 million came too late to make dramatic expansion possible, as many families already had made alternate arrangements.

The money — which nearly doubled the system’s $2.4 million budget for summer school — went toward expanding programs for students with disabilities, literacy programs run by community organizations and Summer Bridge, the program for incoming ninth-graders.

Officials also used the funding to make summer school more attractive to families by offering some bus transportation and more afternoon enrichment programs that run until 5 p.m., a boon for working parents who otherwise would have to pick up their children at summer school’s 1 p.m. dismissal.

Additionally, the money allowed officials to expand — from 60 seats to more than 100 — a pilot program for students with profound struggles in reading.

That change made a significant difference for Kay Frazier, whose grandson, a rising fourth-grader, initially was not invited to summer school because he was too far behind in reading.

An invitation arrived after the council allocated extra funds. Frazier — who knew the boy needed help but couldn’t afford private tutoring — was relieved. She said her grandson has thrived.

“The program I feel really helped him, did wonders for him,” Frazier said. “I know it works because he comes home and tells me, ‘I’m learning new words, I’m learning big words.’ . . . He never did that before.”

Frazier said she wasn’t surprised that the school system fell short of its enrollment target. By the time officials announced all students could attend, many families had made other plans.

“People were very confused,” she said.

City officials have not disbursed the extra $2 million the council approved for charter schools’ summer programs. Officials said they plan to divide that money among charters based on each school’s certified summer enrollment.