The city has approved more than 10,000 new full-day pre-kindergarten seats in privately run centers, Mayor Bill de Blasio announced Friday, continuing the city’s all-out sprint to make 53,000 seats available by September.

The locations of those 10,400 free pre-K seats, which will be managed by more than 200 community-based organizations, have come under fresh scrutiny this week. Officials said Friday that about half of the newly approved seats are located in low-income neighborhoods, and noted that hundreds were coming to Crotona-Tremont in the Bronx and to Flushing and Jamaica in Queens.

At a hearing on Wednesday, some City Council members said they were concerned that neighborhoods with overcrowded schools and a short supply of CBOs may be left with few local pre-K options. Today, de Blasio acknowledged that the demand in some neighborhoods may outstrip the supply, at least in the first year of the expansion.

“This is one of the biggest challenges in this process,” he said, adding that some families will have to travel out of their school zones to find available seats. “It’s not always the perfect geographical match.”

The new batch of CBO seats, which were approved by the Panel for Educational Policy on Thursday, brings the total of such seats to 25,000. About 20,000 seats inside public schools have already been approved, and an additional 8,000 pre-K seats inside other nonprofits, religious schools, charter schools, and more public schools still must be approved for the city to meet its targets.

The pre-K seats the city has approved so far are spread across all five boroughs. Of the roughly 45,000 seats, Brooklyn has the most with 15,100, Queens has 10,700, and the Bronx has 10,300. Meanwhile, Manhattan has 6,400 and Staten Island has 2,400.

The city has also continued to face questions about how officials will guarantee that the privately run pre-K sites match the quality of the pre-K classes at public schools.

Deputy Mayor Richard Buery said Friday the city’s quality control began with a “rigorous screening process” that considered the facilities, staffing levels, and experience of the private groups that applied to offer pre-K next year. About 40 percent of those applications were rejected, Buery said.

Once the sites are up and running, city workers will inspect them at least twice per year in visits that may be planned or unannounced, Buery said. The city will hire more inspectors to keep tabs on all the new sites, de Blasio said. And the Department of Education will provide summer training and ongoing support to the CBO teachers, he added.

“This is an extraordinarily large effort and we have resourced it accordingly to guarantee the quality control,” de Blasio said.

Another concern has been the longstanding gap between the salaries of pre-K teachers at privately run sites and those at public schools, who earn full unionized teacher salaries.

The city announced last month that it would increase the pay of CBO teachers to push them closer to public school salaries. But since then, the city forged a deal with the teachers union that could eventually raise public-school teachers’ salaries by 18 percent. A City Hall spokesman said the CBO teachers will not get equivalent raises, and that the city’s goal has been to decrease the pay gap between the groups, not to create full parity.

The deadline to apply for the public school seats has passed, but families can contact schools directly about open seats beginning next month.

Families can now fill out a universal form and submit it in person to any CBO. Beginning next Tuesday, they will be able to apply online. The city is encouraging families to apply for the CBO seats by the end of the school year, but they will continue to accept applications throughout the summer.

Don’t miss the latest news on New York City schools: follow Chalkbeat New York on Facebook