Howard University is shedding about 75 staff positions in a re­organization that comes at the same time a rare public rift on the board of trustees over the school’s finances and management has riveted students, faculty and alumni.

Kerry-Ann Hamilton, a university spokeswoman, wrote in an e-mail that 53 employees had been laid off as of June 7. She said none was a member of the academic faculty. Howard had 3,636 non-faculty employees at the university and its hospital as of Friday, Hamilton said.

The cuts are part of an “administrative renewal” plan that trustees approved two years ago to improve efficiency. “This process requires that we make difficult decisions,” she said.

The university gave no information about which positions were cut or how much money would be saved. The other planned position cuts may occur over a period of months.

The job cuts at Howard come as the university community has turned its attention to the financial well-being of the historically black college in Northwest Washington, which functions as a private institution but receives more than a quarter of its annual operating funds through a federal appropriation. The concerns have grown since the June 7 disclosure of a letter by a Howard trustee, who warned that the school “is in genuine trouble.”

The university “will not be here in three years if we don’t make some crucial decisions now,” board Vice Chairwoman Renee Higginbotham-Brooks wrote in the April 24 letter to trustees.

Higginbotham-Brooks, a Fort Worth lawyer and Howard graduate, has given the university $350,000 and raised hundreds of thousands more — evidence, she said, of her loyalty to the institution. She cited falling student enrollment, cuts to the federal appropriation and expenses from the university hospital as major concerns.

Board Chairman Addison ­Barry Rand fired back Monday. In his own missive, Rand wrote that the publication of the Higginbotham-Brooks letter had painted “an unduly alarming picture of the University’s condition.” Rand, who is chief executive of AARP, said Howard “remains academically, financially and operationally strong.”

A roster on the university’s Web site shows the board has 33 members, including Howard President Sidney A. Ribeau, who has held office since 2008. Among the notables on the board are former Virginia governor L. Douglas Wilder and Atlanta Mayor M. Kasim Reed.

Ribeau, Rand, Higginbotham-Brooks and numerous other trustees declined requests for interviews. The university has not made any of its top officers available for comment since June 7.

There is consensus that Howard, founded after the Civil War under a charter Congress enacted in 1867, faces significant fiscal challenges. Its total student enrollment fell 5 percent in fall 2012, to 10,002. Its federal appropriation of $234 million a year — a funding arrangement rare in higher education — is expected to be cut about 5 percent because of the federal budget sequester. Ribeau temporarily suspended some payments to employee retirement plans and took other steps this year to save money.

The board debate and staff layoffs have sparked intense questions within the university community. Some have taken comfort from Rand’s letter. Others wonder whether there are more problems yet to be unearthed.

Gregory Jenkins, a physics professor, said he learned of the Higginbotham-Brooks letter June 8 via e-mail as he was on a research visit to Senegal in west Africa. He said he worries about spending cuts. “We’re going down a slope,” Jenkins said. “I don’t know why. It just seems like things aren’t steady yet.”

He added: “We want the best for our university. We want the reputation to be maintained. We want families to know ‘Hey, when you send your kids to Howard, they’re getting a quality education.’ ”

Anthony Miller, a student government leader who graduated from Howard in May with a bachelor’s degree in economics, said he trusts the university leadership.

“There’s a lot of work that needs to be done,” Miller said. “Howard’s not without its problems. But these problems are not new. We have a good future ahead of us. . . . I don’t think for a moment that Howard would not be around in three years. That’s not real.”

Chris Washington, a 1992 Howard graduate and president of the university’s alumni association, said he was disappointed that the Higginbotham-Brooks letter became public. But he said he wanted to capi­tal­ize on the moment to push graduates to get more involved with their alma mater. “They’re fired up,” Washington said. “They can’t believe this is happening.”

James E. Silcott, of Los Angeles, is a Howard donor and 1957 graduate who served on the board of trustees from 2003 to 2009 alongside Higginbotham-Brooks and Rand. He said he was shocked that the vice chairwoman was so outspoken in her letter. “She’s always been demure and quiet,” he said. Silcott said he agreed with much of what she wrote.

“There’s a lot of alums out there that are sitting on their pocketbooks,” Silcott said. “They’re not going to give Howard any money the way things are being done.”

Michael L. Lomax, president and chief executive of the United Negro College Fund, known as UNCF, called the Higginbotham-Brooks letter “intemperate” and said he had “great confidence” in Ribeau’s leadership. Lomax said his daughter is transferring to Howard this year from Agnes Scott College in Decatur, Ga. “I have every confidence she is going to get an extraordinary education,” Lomax said.