At least five Democratic presidential candidates called for Supreme Court Associate Justice Brett Kavanaugh to be impeached after a new report about alleged sexual misconduct from his college years. President Trump, meanwhile, stood by Kavanaugh and said the Justice Department should "rescue" him.

Over the weekend, multiple Democratic presidential candidates, including Elizabeth Warren, Kamala Harris, Julián Castro, Cory Booker and Pete Buttigieg, called for Kavanaugh to be impeached. Kavanaugh has not responded to the latest report, but previously denied all accusations.

"Last year the Kavanaugh nomination was rammed through the Senate without a thorough examination of the allegations against him," Warren tweeted. "Confirmation is not exoneration, and these newest revelations are disturbing. Like the man who appointed him, Kavanaugh should be impeached."

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Harris and Castro both accused Kavanaugh of lying under oath during his Senate confirmation hearings.

I sat through those hearings. Brett Kavanaugh lied to the U.S. Senate and most importantly to the American people. He was put on the Court through a sham process and his place on the Court is an insult to the pursuit of truth and justice. He must be impeached. — Kamala Harris (@KamalaHarris) September 15, 2019

It’s more clear than ever that Brett Kavanaugh lied under oath. He should be impeached. And Congress should review the failure of the Department of Justice to properly investigate the matter. https://t.co/Yg1eh0CkNl — Julián Castro (@JulianCastro) September 15, 2019

In a statement obtained by CBS News, Joe Biden called for further investigation into Kavanaugh and "the truthfulness of his testimony to Senate." "We need to get to the bottom of whether the Trump Administration and Senate Republicans pressured the FBI to ignore evidence or prevented them from following up on leads relating to Justice Kavanaugh's background investigation," the former vice president said.

He also applauded the women who have come forward with accusations against Kavanaugh, saying they "deserve to be treated with dignity and be listened to."

On Saturday, the New York Times published an essay adapted from a book excerpt that claimed one of Kavanaugh's Yale classmates allegedly saw him with his pants down at a drunken dorm party, with friends pushing his penis into a female student's hands, when Kavanaugh was a freshman. According to the essay, the classmate told this story to senators and the FBI, but the FBI did not investigate it.

During Kavanaugh's confirmation process, another Yale classmate, Deborah Ramirez, said Kavanaugh pulled down his pants at another drunken dorm party and thrust his penis at her. She said she swatted it away. The Times essay said it had found additional corroboration for Ramirez's story, with seven people saying they heard about the incident long before Kavanaugh became a federal judge.

On Sunday, the New York Times issued an editors' note that stated an earlier version of the essay "did not include one element" of the book's account of the incident. "The book reports that the female student declined to be interviewed and friends say that she does not recall the incident," the editors' note states. "That information has been added to the article."

The New York Times also deleted a previous tweet that promoted the essay, calling it "offensive."

We deleted a previous tweet regarding this article. It was offensive, and we apologize. https://t.co/gbUdweKbDg — New York Times Opinion (@nytopinion) September 15, 2019

Buttigieg told CBS News late Sunday that "it's appalling to learn that the GOP curtailed the FBI investigation" and that "[t]he American people deserve to know who was involved ... and we must get answers fast as to why witnesses with key information were not interviewed."

The first public accusation against Kavanaugh last year came from Christine Blasey Ford, a psychology professor. She said that when she and Kavanaugh were in high school, he drunkenly held her down on a bed, groped her, tried to pull off her clothes and covered her mouth when she tried to scream. Kavanaugh said the alleged incident never happened.

Blasey Ford and Kavanaugh testified before Congress about the accusation, and both said they were "100%" certain of their version of events. The FBI investigated the accusations against Kavanaugh, but agents did not interview him, Blasey Ford or dozens of people who said they had corroborating evidence.

The FBI has no comment on the new report but CBS News correspondent Jeff Pegues notes there were limits on what the FBI was able to do because it was an abbreviated investigation with the timetable set by Congressional leadership.

President Trump shakes hands with Supreme Court Justice Brett Kavanaugh, before a ceremonial swearing-in in the East Room of the White House in Washington, on Mon., Oct. 8, 2018. AP

Kavanaugh was confirmed in October 2018 by the smallest Senate vote margin in nearly 140 years.

Mr. Trump defended Kavanaugh during the confirmation process and mocked Blasey Ford's testimony. After this latest accusation, the president said that Kavanaugh should take legal action.

"Brett Kavanaugh should start suing people for libel, or the Justice Department should come to his rescue," Mr. Trump tweeted.

The president also tweeted that Democrats and the accusers were trying to influence Kavanaugh's Supreme Court decisions and "scare him into turning Liberal."

An impeachment process for a Supreme Court justice would be similar to that of a president, with the House voting on impeachment and the Senate deciding on removal. So while the Democrat-controlled House could impeach Kavanaugh, he's unlikely to be removed by the Republican-led Senate. Only one Supreme Court justice has ever been impeached — Samuel Chase, in 1805 — and none has been removed.

Blasey Ford's attorney, Deborah Katz, told CNN last year that Blasey Ford does not want Kavanaugh impeached, even if Democrats take control of Congress.

Katz and a spokeswoman for the Supreme Court did not immediately comment to CBS News.