Former state attorney general Martha Coakley said Tuesday that she has no interest in becoming president of Suffolk University, upending plans by some trustees who were courting her as a possible replacement for the college’s embattled leader, Margaret McKenna.
The announcement was one of several twists in the public battle being fought at Suffolk, a downtown university known for its tumultuous recent history.
The region’s accrediting agency, whose approval can affect the flow of federal dollars to the school, intensified pressure on the school to explain the ugly row between the governing board and its president. And Suffolk students and staff rallied in support of McKenna.
For Coakley, now a lawyer at the Boston firm Foley Hoag, it was her first public comment since it was revealed Thursday that some trustees want to oust McKenna.
“I would like to clarify that I am not a candidate for the role of president of Suffolk University nor will I be,’’ she said in a brief statement.
Trustees are scheduled to meet Friday to decide the fate of McKenna, who has refused to resign. McKenna is the fifth president in five years, including longtime leader David Sargent, president James McCarthy, and two interims.
“I have respect for Margaret and Martha, and in view of the circumstances I can understand Martha’s decision,” said trustee James T. Morris, founding partner of the Quinn & Morris law firm and 1971 Suffolk Law School graduate.
Trustee Jennifer Nassour, former chairwoman of the state Republican Party, said she was glad Coakley isn’t interested because “she does not have the managerial skills to lead a university.
“We need a board that supports the president,” Nassour added. “We need to air our differences behind closed doors and come out smiling as a united front.”
Other board members, including chairman Andrew Meyer, declined to comment on Coakley’s statement.
Scores of Suffolk students, faculty members, and staff rallied in support of McKenna.
“No trust in the trustees,” the students chanted as they gathered outside a meeting on campus.
Marty Elmore, the program coordinator for the Suffolk Center for Academic Access and Opportunity, said McKenna is the only president in recent history to speak about the greater need for diversity at the school.
Several students criticized trustees for not involving students in their discussions.
“We have a president who actually cares about us,” said sophomore Jacob Marino. “It’s our school, it’s our money. We should have a say in who runs it.”
Suffolk representatives did not respond to requests for comment about the rally.
The trustees said they are looking out for the best interest of the university and concerned about McKenna’s “disrespectful manner” and several financial decisions that they say could create the first deficit the school has faced in at least five years.
The controversy could have wide-ranging repercussions.
The Commission on Institutions of Higher Education, the accreditation arm of the New England Association of Schools and Colleges, wants Suffolk to submit a report on the imbroglio, said Barbara E. Brittingham, the commission’s president.
“The commission gets a lot of reports, so it wouldn’t ask lightly,” she said.
Brittingham declined to be specific about any deadlines for Suffolk to respond but said it should be “sooner than later.”
Brittingham said the school’s current problems appear related to an issue that was identified in the commission’s evaluation of Suffolk, completed as part of an accreditation in early 2014. At the time, the commission had raised questions about the school’s governing structure, and recommended Suffolk clarify the responsibilities and authorities of the board and the administration.
The commission wrote in 2014 that it was encouraged the board intended to rewrite the school’s bylaws later that year, to create a new set of rules “based on best practices of similar institutions.” The commission also was pleased that the board “recognizes the need to return to a more appropriate oversight and advisory role.”
Two years later, however, the bylaws have not yet been rewritten, Suffolk administrators have confirmed.
The existing bylaws, which are 21 years old, appear to place significant management authority in the hands of the board, such as the power to make “appointments of professors, instructors and other persons employed in an administrative or executive capacity.”
The bylaws of several other local colleges — MIT, Brandeis University, Emerson College, and Tufts University — state emphatically that the school president is the chief executive officer of the institution, a post that traditionally holds hiring and firing powers.
Rather than being a CEO, Suffolk’s president is the “official head” of the school’s “educational system,” according to Suffolk’s bylaws.
Richard D. Legon, president of the Association of Governing Boards of Universities and Colleges, said trustees have “the ultimate responsibility to protect the assets of the institutions.”
“Having said that, most boards recognize — or at least they should — that they are not management, they are fiduciaries; they are responsible for making sure there is a strong and effective CEO in place who leads the institution,” he said.
Analysts at Moody’s Investors Service said Tuesday that they are monitoring the situation at Suffolk. “A reputation is what drives student demand and donor confidence,” said Susan Fitzgerald, associate managing director at Moody’s.
The school’s current bond rating is Baa2, which carries the potential for credit risk.
Globe correspondent J.D. Capelouto contributed to this report. Laura Krantz can be reached at firstname.lastname@example.org. Follow her on Twitter @laurakrantz. Mark Arsenault can be reached at email@example.com. Follow him on Twitter @BostonGlobeMark.