“We recognize that our decision to accept this loan may draw criticism from some quarters of the community,” said the school, which has a $53.4 million endowment, “but are fully united in our decision.”

The Pingry School, with campuses in Short Hills and Basking Ridge, N.J., and a roughly $80 million endowment, said it would keep the money it had received to pay faculty and staff members, as intended by the federal program.

St. Andrew’s, in Potomac, which reported a roughly $9 million endowment in a 2017 tax filing, said it would put the money toward salaries “to ensure retention of our full faculty and staff, including hourly employees and coaches, during this very challenging and uncertain time.”

Neither school disclosed how much it had received in loan money.

Run by the S.B.A., the $660 billion assistance effort — formally known as the Paycheck Protection Program — has been troubled by technical glitches, partisan squabbling and widespread confusion over who is worthy.

Large public companies have leaned on their relationships with banks, which are issuing the loans, while many Main Street businesses like ice cream stores, salons and neighborhood restaurants have often found themselves left out.

That tension is playing out in miniature in the private school world. While there is no suggestion that any school used political ties to bolster its application, some bigger institutions are able to tap board members and donors with connections to banks.

“It’s kind of a wild thing that’s happening — you can see the pitfalls with the program,” said Jennifer S. Danish, head of school at Grace Episcopal Day School in Kensington, Md., which she said served mostly middle-class students. “If you have a board member or a connection with a big bank, you’re more likely going to get it.”