Mr Kavanaugh has emphatically denied Christine Blasey Ford's allegation that he sexually assaulted her at a gathering when they were teenagers.
The Senate's Democratic leader, Chuck Schumer of NY, accused Kavanaugh of delivering a "partisan screed" during the judiciary committee hearing last week.
Sen. John Kennedy of Louisiana, a Republican member of the Judiciary Committee, said Kavanaugh has only been responding to Democratic attacks.
In his testimony, Kavanaugh vehemently denied Ford's claim.
Swetnick, who is represented by Michael Avenatti, has alleged that Judge and Kavanaugh were present at a party in the early 1980s where, she says, she was gang-raped.
Among the allegations McConnell criticized was one brought by a "tabloid lawyer" he did not name whose client has alleged she was victimized at a party attended by Kavanaugh friends and for which "there conveniently happened to be zero witnesses".
Kavanaugh has denied claims of sexual misconduct by three different women - Ford, Deborah Ramirez and Julie Swetnick.
What he's said: "I agreed to support him before all of this came out".
Kavanaugh and his accuser, Christine Ford of California, were brought before the committee on September 24 to testify.
He said that the Kavanaugh hearings where more than just a Supreme Court nominee, but rather a huge cultural moment in the United States.
But the senators whose votes hold the key to confirmation wanted the White House to know they expect those interviews to be a start, not necessarily the full extent of the investigation.
US President Donald Trump surrounded by staff, speaks from the Rose Garden of the White House in Washington, DC, remarking on the United States-Mexico-Canada Agreement on October 1, 2018.
But Sen. Chuck Grassley, R-Iowa, chairman of the Judiciary Committee, said Kavanaugh could be excused for showing passion.
Trump also said in response to a reporter's question that it "would not be acceptable" if Kavanaugh had lied to Congress during his testimony. During the hearing, Kavanaugh acknowledged sometimes drinking too many beers in high school but said he did not have a problem with alcohol and never forgot his behavior. At his first Supreme Court confirmation hearing, September 4, he portrayed himself as a neutral arbiter of the law who is above politics, telling the Judiciary Committee that the Supreme Court "must never be viewed as a partisan institution".
The most senior Democrat on the Senate's Judiciary Committee, Dianne Feinstein, has sent a letter urging the White House to release the written directive sent by President Trump to the FBI launching the investigation.
As the investigation is not a criminal one, the FBI will not say whether they believe the allegations are true. He said he may run - either as a Republican or an independent - if no one else does. He said he did not want the probe to become a "witch hunt" and that it should be completed quickly.
A vote to confirm Mr Kavanaugh has been delayed as the FBI investigates the claims, which he denies. After facing a wave of criticism, Trump appeared to relinquish this strict control over the probe, telling the bureau that it would have the leeway to investigate whichever leads it deems relevant.
But Trump and Republicans have defended Kavanaugh, and Trump again stood by his nominee on Tuesday, saying that the way the allegations were being treated shows it's a "very hard time" for young men.
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