Sarah Huckabee Sanders responded by saying the White House "stands with Kavanaugh" - but Trump couldn't leave it at that.
The Washington Post has not independently verified her allegations.
Kavanaugh has repeatedly denied all of the allegations against him.
Asked if he had participated in or was aware of any gang rape at a party he attended, he said, "That's totally false and outrageous".
Swetnick's sworn statement was released about 24 hours before Dr. Christine Blasey Ford was scheduled to testify before the Judiciary Committee, and hours after Ford's lawyers released four sworn statements from supporting witnesses corroborating her claim of sexual assault-statements that the Republican-led committee has shown no interest in examining. Murkowski did not weigh in with a public statement Thursday; Collins told CNN that the allegations should be investigated by the committee and that she takes them very seriously; Corker told reporters Wednesday morning he did not know enough about the latest allegations to comment.
Swetnick's statement implicates Kavanaugh and his friend Mark Judge in attempting to ply women with alcohol and drugs to take advantage of them sexually.
The claim came days after California professor Christine Blasey Ford alleged that as a teen-ager Kavanaugh held her down, put his hand over her mouth and tried to remove her clothing at a house party and Yale student Debbie Ramirez alleged that Kavanaugh exposed himself to her at a party in college.
Iran arrests 'large network' over Ahvaz attack
Fars and IRNA news agencies said on Monday five attackers were killed, not four as previously reported by state media. It answers to Ayatollah Khamenei and has an estimated 125,000-strong military with army, navy and air units.
"What's important here isn't the lawyer, what's important here is the person who claims she's been harmed", Grassley said.
Kennedy, Cruz and others said the potentially crucial hearing with Kavanaugh and Ford, the first woman to accuse Kavanaugh, will go forward on Thursday.
Some also pointed out that Swetnick's claims matched those of an ex-girlfriend of Mark Judge, Kavanaugh's high school classmate who Swetnick named as allegedly joining Kavanaugh in gang-raping girls at house parties in the 1980s. Kavanaugh graduated from Georgetown Prep in 1983. She saw them to be "extremely close friends" who were "consistently" together at social gatherings. "Shortly after the incident, I shared what had transpired with at least two other people", Swetnick said. If she had placed it when she herself was in high school, Kavanaugh would have been around 14 years old.
She said she observed Kavanaugh drinking "excessively" at numerous parties and engaging in "abusive and physically aggressive behaviour toward girls, including pressing girls against him without their consent, "grinding' against girls, and attempting to remove or shift girls' clothing to expose private body parts".
"We're not going to vote on confirmation until Tuesday, so there's plenty of time for that interview to take place and I suspect that the longer this hangs out there the more accusations will occur, including those like Ms. Ramirez which by her own terms she's not sure whether she correctly identified Brett Kavanaugh", he said.
"I have a firm recollection of seeing boys lined up outside rooms at many of these parties waiting for their "turn" with a girl inside the room", she said in the statement.
In the intervening years, Swetnick has mostly remained in the Washington area, where she has worked as a web and information technologist. She said that she has inactive clearances at the State Department, the Department of Justice, Homeland Security and Customs and Border Protection.