Besieged Suffolk University president Margaret McKenna met for four hours Wednesday with the college’s trustees chairman, Drew Meyer, in an effort to resolve their highly public dispute, as worries grew over the damage it is causing to the school’s reputation.

The meeting took place as Mayor Martin J. Walsh waded into the ugly tiff for the first time, offering strong praise for McKenna’s leadership and urging board members to “work this out.’’

A brief statement from the university, while short on specifics, hinted that the spat might be winding down. It said McKenna and Meyer plan to continue to meet and work toward a proposal they hope to present jointly Friday when the governing board is expected to decide whether to oust McKenna after only seven months on the job.

“Chairman Meyer and President McKenna strongly agree that the interests of Suffolk University, its students, faculty, staff and alumni, must come first,’’ said the statement from Suffolk spokesman Greg Gatlin.

Walsh, meanwhile, said McKenna has done a “great job’’ as president of Suffolk. He said he called several members of Suffolk’s board on Wednesday, and urged them to find a way out of the morass.

“I don’t think it’s good for any university to have these squabbles on the front page of the paper,’’ Walsh said in a Globe interview. “My message to the board — and I’ve been talking to them — is to sit down and have a conversation and figure this out, work this out.

“They’re an important institution for our city, so I would like to see this thing resolved and not play out in a nasty fashion in the press, where attorneys have to get involved and PR people are involved.’’

It is unclear whether the two trustees who attended Wednesday’s meeting, Meyer and Jim Morris, might have tried to urge McKenna to accept a settlement or may be open to the idea of keeping her in the job. Attorneys for both sides also attended.

“Everything is on the table,’’ said one person with knowledge of the meeting.

The meeting occurred the day after former attorney general Martha Coakley, who was considered a likely replacement for McKenna by some board members, said she was not interested in running the private downtown school, which has an enrollment of about 9,000 students.

McKenna is in trouble after some trustees, including Meyer, accused her of having an abrasive style and making unauthorized expenditures that set the school on track to run a deficit.

But some trustees’ handling of the matter has drawn outrage from faculty, students, and alumni. They say some board members have attacked Mc­Kenna without seeking the opinions of the full board and largely via the news media instead of directly with McKenna.

There is also growing dissension on the board.

Trustee Daniel F. Conley, who is the Suffolk County district attorney and a Suffolk Law School graduate, said Wednesday that he has been traveling and learned everything about the controversy from media accounts.

“I am disappointed to see that the relationship between some members of the board and President McKenna has deteriorated so severely,’’ Conley said. “I plan to attend Friday’s trustee meeting to determine the facts, to carefully consider, discuss, and evaluate.’’

Another trustee, John Fernandez, wrote to the other trustees expressing similar concerns.

“We need a plan forward we agree upon as a board and not just a small group or the executive committee,’’ Fernandez, president and CEO of the Massachusetts Eye and Ear Infirmary, wrote in an e-mail to other board members that was obtained by the Globe.

Fernandez also wrote that he would like to discuss “what steps we will take to manage the perceptions of Suffolk and its board members.’’ The agenda for Friday’s board meeting, which is closed to the public, says trustees will consider “termination of Margaret A. McKenna’s employment immediately with the university in accordance with the terms and conditions of her employment agreement.’’

The terms of the contract remain unclear. McKenna has a five-year deal and makes about $650,000 per year. She started her job in July and is the fifth president in five years, including longtime leader David Sargent, interim Barry Brown, president James McCarthy, and interim Norman Smith.

Also Wednesday, Suffolk’s faculty senate sent a letter to trustees expressing support for McKenna and calling for Meyer’s resignation.

The faculty also urged the board to proceed immediately with organizational reforms called for by the regional accrediting agency in its 2014, which include updating the school’s bylaws and ensuring the board is not overly involved in daily university business.

Smith, the interim leader before McKenna was hired, said there were financial concerns when he led Suffolk during the 2014-15 school year but he was able to balance the budget by eliminating some senior administration positions. Those who were pushed out included staffers who raised money for the school.

Smith, now interim president of Elmira College in New York, said the board’s level of involvement is “comparable’’ to that at other schools.

“They were looking over their shoulders an awful lot more before I got there than some boards do, but I think they had reason to be concerned,’’ added Smith, who said Suffolk trustees have not asked him to serve as an interim again.

McKenna is a former Boston School Committee member, and Walsh said he would have reappointed her, had she not left in 2014 to become chair of the state Board of Elementary and Secondary Education.

“In what I’ve seen of her in her role as a president, I think she has done a lot to promote the school in a very short period of time,’’ Walsh said. “She’s somebody who I see out there visibly in the community, advancing the school and has a good story to tell about the school.’’

Laura Krantz can be reached at laura.krantz@globe.com. Follow her on Twitter @laurakrantz. Mark Arsenault can be reached at mark.arsenault@globe.com. Follow him on Twitter @bostonglobemark