Kamehameha Schools has presented a “strong, substantial” financial offer in hopes of settling a lawsuit in which more than 30 former students accused a psychiatrist of sexually abusing them decades ago, the institution’s chairman said Wednesday.

But a lawyer for the plaintiffs disputed the characterization of the offer.

Micah Kane, who heads Kamehameha’s board of trustees, said he was “hopeful” as a second round of mediation sessions began Wednesday in an attempt to settle the 2016 lawsuit.

“Everybody’s come to the table in the spirit of trying to come to an agreement,” Kane told the Honolulu Star-Advertiser.

He said more than one offer has been presented and described the current one as substantial. Kane declined to be more specific.

Mark Davis, an attorney for the plaintiffs, disputed Kane’s description.

“We are legally prohibited from discussing the amounts offered in mediation, but we disagree with his characterization,” Davis said in a statement. “Nonetheless, we hope they eventually will step up to the plate and do what is right.”

A first round of mediation talks last year was unsuccessful, and the case currently is scheduled to go to trial in June.

But since the last talks ended, Kamehameha has received widespread criticism, including from alumni, after the Star-Advertiser disclosed that the school did not conduct a broad investigation once the allegations started surfacing in 1991, did not report the allegations to authorities and over the years and did not contact the former students to offer assistance.

The school has acknowledged that the plaintiffs were abused by Dr. Robert Browne, who killed himself in 1991 after being confronted by one of the former students. Browne was a psychiatric consultant who treated hundreds of troubled students from the late 1950s to the early ’80s.

Thirty-four plaintiffs — most of them former Kamehameha students — have sued the school; St. Francis Medical Center, where Browne was employed; and his estate, alleging that the defendants were grossly negligent in failing to keep the plaintiffs safe. The plaintiffs also said the school attempted to conceal the abuse for years.

The defendants have denied wrongdoing.

Kane said Kamehameha Schools feels strongly that the healing process should begin. All five trustees participated in Wednesday’s talks in person or through teleconferencing, according to Kane.