Justice Elena Kagan said on Friday that the Supreme Court should adopt a code of ethics, saying that “it would be a good thing for the court to do that.”

Her comment, part of a wide-ranging live-streamed public interview at Notre Dame Law School, came on the day ProPublica reported that Justice Clarence Thomas had twice attended an annual event for donors organized by the conservative political network established by the billionaire industrialists Charles and David Koch.

Justice Kagan did not discuss the report, but she said that an ethics code “would, I think, go far in persuading other people that we were adhering to the highest standards of conduct.” She added that “I hope we can make progress.”

G. Marcus Cole, the law school’s dean, asked her to identify the holdout among the justices.

She refused, saying the justices’ deliberations are private. “What goes on in the conference room stays in the conference room,” she said. She added that she did not want to suggest that there was a single holdout.

“There are, you know, totally good-faith disagreements or concerns, if you will,” she said. “There are some things to be worked out. I hope we can get them worked out.”

Dean Cole, noting that the court had in recent terms overturned major precedents on abortion and affirmative action, asked whether the justices’ commitment to adhering to earlier decisions had split them along ideological lines.

Justice Kagan said she hoped that was not the case, but she did not dispute the premise of the question. “You’re right that there have been times recently where there have been ideological divides with one side overturning precedent.” But she added: “I’m hopeful that it won’t have that year after year, case after case. At least it shouldn’t.”

She suggested that overruling precedents soon after a change in the composition of the court undermined its legitimacy.

“Adherence to precedent is important because it prevents the court from looking like a political actor, like an ideologically driven actor,” she said, adding that “when courts just overrule things, willy-nilly, it’s usually because, or sometimes it’s because, new judges have come on the scene.”

That, in turn, does harm to the judiciary’s authority, Justice Kagan said. “It makes people think that courts are just sort of making it up on the fly,” she said. “And that’s an extremely damaging thing for the judicial system and, I think, for our country.”

Dean Cole asked about a striking statement from Chief Justice John G. Roberts Jr. in his majority opinion in June rejecting President Biden’s student loan forgiveness program. “I don’t think I have ever read such an exchange between a majority opinion and a dissent before,” the dean said.

The chief justice, objecting to Justice Kagan’s dissent in the case, wrote that “it has become a disturbing feature of some recent opinions to criticize the decisions with which they disagree as going beyond the proper role of the judiciary.”

Justice Kagan was unapologetic. “I don’t think that that’s disturbing at all,” she said. “I think it would be disturbing if a dissent that thought that the court had gone beyond the proper role of the judiciary — it would be disturbing if you didn’t say that — if you pulled your punches.”

But she added that she holds Chief Justice Roberts in high regard.

“I admire him as a person,” Justice Kagan said. “I admire him as a judge. I admire him as the institutional leader of the court. So this was — there was nothing personal about this.”

Dean Cole asked whether news reports are unduly focused on decisions in which the justices split 6 to 3 along partisan lines.

Justice Kagan said the court is often unanimous or scrambled in unusual alignments. But she said the recent run of 6-3 cases was notable. “To be completely honest,” she said, “it has to be said that some of the more important cases do fall along pretty predictable lines.”

She ticked off some of those cases, noting ones on affirmative action, student loans, L.G.B.T.Q. rights, abortion and climate change.

“When all of these are falling six to three,” she said, “it doesn’t strike me as surprising that people will talk about that.”