Gordon Gee also took shots at schools in the Southeastern Conference and the University of Louisville, according to the recording of the December meeting of the school's Athletic Council that The Associated Press obtained under a public records request.
The university called the statements inappropriate and said Gee is undergoing a "remediation plan" because of the remarks.
Gee was on a long-planned family vacation and unavailable for comment, Ohio State spokeswoman Gayle Saunders said. He 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 in the statement. "They were a poor attempt at humour and entirely inappropriate. There is no excuse for this and I am deeply sorry."
Gee, who has taken heat before 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, several other athletic department members, 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 as it sought to retain its independent status in college football. In September, the school announced that it would join the Atlantic Coast Conference in all sports except football but would 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 executive vice-president, 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.
Notre Dame spokesman Dennis Brown called the remarks regrettable, especially the reference to Joyce, "who served Notre Dame and collegiate athletics so well and for so long." Gee contacted Notre Dame's president, the Rev. John Jenkins, to offer an apology, which was accepted, Brown said Thursday in an email, declining to say when the apology was made.
Notre Dame has a storied collegiate football history and is perhaps the nation's pre-eminent Roman Catholic university. Ohio State, with about 56,000 students on its main campus, is among the country's biggest universities, and it has its own long football tradition.
A message was left with Smith, the Ohio State athletic director who attended the December meeting and who also is a 1977 Notre Dame graduate. NCAA President Mark Emmert declined to comment, saying he hadn't heard the remarks.
Ohio State's 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.
Gee was introduced by Athletic Council then-chairman Charlie Wilson, and Gee's name and introduction are included in written minutes of the meeting. His comments drew laughter, at times loud, occasionally nervous, but no rebukes, according to the audio.
Ohio State trustees learned of Gee's "offensive statements" in January, met with the president at length and created the remediation plan for Gee to "address his behaviour," board president Robert Schottenstein said in a statement.
Comments by a university leader about "particular groups, classes of people or individuals are wholly unacceptable," Schottenstein said. "These statements were inappropriate, were not presidential in nature and do not comport with the core values of the university."
Gee has gotten in trouble before for offhand remarks, most recently during a memorabilia-for-cash and tattoos scandal under football coach Jim Tressel's watch.
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 co-ordinating the school's many divisions to the Polish army, a remark that a Polish-American group called bigoted and ignorant.
In 1992, in a moment of frustration over higher-education funding, Gee told a student newspaper reporter, "the governor's a damn dummy." Then-Gov. George Voinovich laughed it off, and the two became allies.
Gee was named the country's best college president in 2010 by Time magazine, and he has one of the highest-profile resumes of any college leader 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.
Gee 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," which 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.
Louisville spokesman Mark Hebert said the university accepted Gee's apology but planned to forward Gee information about the upward trajectory of its academic and athletic programs.
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 the audience that speculation about the SEC "remains right here," according to the recording.
Gee took a swipe at Big Ten Commissioner Jim Delany, 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 Delany 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."
Gee's comments "were inappropriate and in no way represent the opinions of the conference," Delany said in a statement, adding he had apologized to Notre Dame and the SEC.
Associated Press writers John Seewer in Toledo, Tom Coyne in South Bend, Ind., Janet Cappiello in Louisville, Ky., and Stephen Hawkins in Irving, Texas, contributed to this report.