At the December meeting of the school's Athletic Council, Gordon Gee also took shots at schools in the Southeastern Conference and the University of Louisville, according to the recording, obtained by The Associated Press under a public records request.
The university called the statements inappropriate and said Gee is undergoing a "remediation plan" because of the remarks.
Gee apologized in a statement released to the AP.
"The comments I made were just plain wrong, and in no way do they reflect what the university stands for," he said. "They were a poor attempt at humor and entirely inappropriate."
Gee, who has taken heat previously for uncouth remarks, told members of the council that he negotiated with Notre Dame officials during his first term at Ohio State, which began more than two decades ago.
"The fathers are holy on Sunday, and they're holy hell on the rest of the week," Gee said to laughter at the Dec. 5 meeting attended by Athletic Director Gene Smith and several other athletic department members, along with professors and students.
"You just can't trust those damn Catholics on a Thursday or a Friday, and so, literally, I can say that," said Gee, a Mormon.
The Big Ten had for years courted Notre Dame, but the school resisted, seeking to retain its independent status in college football. The school announced in September that it would join the Atlantic Coast Conference in all sports except football. It also agreed to play five football games each year against ACC teams.
In the recording, Gee referred specifically to dealing with the Rev. Ned Joyce, Notre Dame's longtime chief financial officer, who died in 2004.
"Father Joyce was one of those people who ran the university for many, many years," Gee said.
Gee said the Atlantic Coast Conference added Notre Dame at a time when it was feeling vulnerable.
"Notre Dame wanted to have its cake and eat it, too," Gee said, according to the recording and a copy of the meeting's minutes.
Gee was introduced by Athletic Council then-chairman Charlie Wilson, and Gee's name and introduction are included in written minutes of the meeting. Gee's comments drew laughter, at times loud, occasionally nervous, but no rebukes, according to the audio.
The Athletic Council meets monthly during the fall, winter and spring and makes recommendations on athletic policy including ticket prices. December's meeting was at Ohio Stadium.
Ohio State trustees learned of "certain offensive statements" by Gee in January, met with the president at length and created the remediation plan for Gee to "address his behavior," board president Robert Schottenstein said in a statement.
"These statements were inappropriate, were not presidential in nature and do not comport with the core values of the University," Schottenstein said.
Gee has gotten in trouble for his offhand remarks, most recently during a memorabilia-for-cash and tattoos scandal that cost football coach Jim Tressel his job. Tressel had known about allegations that players were trading game paraphernalia for money and tattoos but didn't tell the university in violation of his contract and NCAA regulations.
Gee was asked in March 2011 whether he had considered firing Tressel. He responded: "No, are you kidding? Let me just be very clear: I'm just hopeful the coach doesn't dismiss me." Tressel stepped down three months later.
In November 2010, Gee boasted that Ohio State's football schedule didn't include teams on par with the "Little Sisters of the Poor." An apologetic Gee later sent a personal check to the real Little Sisters of the Poor in northwest Ohio and followed up with a visit to the nuns months later.
Last year, Gee apologized for comparing the problem of coordinating the school's many divisions to the Polish army, an off-the-cuff remark that a Polish-American group called a "slanderous" display of bigotry and ignorance.
Gee has one of the highest-profile resumes of any college president in recent history. He has held the top job at West Virginia University, the University of Colorado, Brown University and Vanderbilt University. He was Ohio State president from 1990 to 1997, and returned in 2007. He earns about $1.9 million annually in base pay, deferred and performance compensation and retirement benefits.
He is a prolific fundraiser and is leading a $2.5 billion campaign at Ohio State. He is omnipresent on campus, attending everything from faculty awards events to dormitory pizza parties. He is known for his bow ties - he has hundreds - and his horn-rimmed glasses.
During his comments to the Athletic Council, Gee also questioned the academic integrity of schools in the Southeastern Conference, and the University of Louisville.
The top goal of Big Ten presidents is to "make certain that we have institutions of like-minded academic integrity," Gee said. "So you won't see us adding Louisville," a member of the Big East conference that is also joining the ACC.
After a pause followed by laughter from the audience, Gee added that the Big Ten wouldn't add the University of Kentucky, either.
During the meeting, Gee also said he thought it was a mistake not to include Missouri and Kansas in earlier Big Ten expansion plans. Missouri has since joined the SEC.
"You tell the SEC when they can learn to read and write, then they can figure out what we're doing," Gee said, when asked by a questioner how to respond to SEC fans who say the Big Ten can't count because it now has 14 members.
Gee noted he was chairman of the SEC during his time as Vanderbilt University chancellor. He also told his audience that speculation about the SEC "remains right here," according to the recording.
Gee took a swipe at Big Ten Commissioner Jim Delaney, one of the most powerful leaders in college athletics, when he answered a question about preserving Ohio State's financial interests in light of Big Ten revenue-sharing plans.
"No one admires Jim Delaney more than I do - I chaired the committee that brought him here," Gee said. "Jim is very aggressive, and we need to make certain he keeps his hands out of our pockets while we support him."
Ohio State president E. Gordon Gee speaks earlier this month during the Ohio State University spring commencement in Columbus, Ohio. Gee told a university committee last December that Notre Dame wasn
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