Another group of protesters stormed toward the doors of the nearby Supreme Court building with raised fists.
Trump has called for tougher libel laws in the past, most recently in a tweet that said he wanted the ability to seek "retribution" after journalist Bob Woodward's explosive book "Fear" detailed Trump's administration as plagued by chaos.
The dispute over Kavanaugh has added fuel to campaigning for the midterm elections in November when Democrats will try to take control of Congress from the Republicans.
Justice Sonia Sotomayor said the nine justices recognize the small world they inhabit, suggesting that the tense atmosphere surrounding Kavanaugh's nomination is unlikely to be replicated on the court. Capitol Police said later in the day that 164 of them were arrested.
"Jerry Nadler will do what Jerry Nadler will do", Hirono said, adding that she would not rule out an effort in the coming months to impeach the high court's newest justice.
A few Republican senators who had wavered over whether to vote for Kavanaugh finally backed him this week, saying they did so in part because a brief FBI investigation found no corroborating evidence of Ford's accusations.
Trump's aggressive defense of Kavanaugh - and more recent attacks against his female accuser - have resonated particularly with white working-class men, who are a shrinking voting bloc nationally but remain a critical segment of Trump's political base.
The nomination process has ripped open the scabs on the never-healed wounds of polarisation on the United States body politic exactly a month before the mid-term elections to Congress that can determine the future of Trump's presidency.
In stressing Kavanaugh's frequent agreement with Judge Merrick Garland on the federal appeals court in Washington, the new justice's backers seem to be suggesting that Kavanaugh's vote can not be taken for granted.
"We made a lot of women real anxious today, but I'm not getting pregnant so I don't care!" Why, now that Kavanaugh has been confirmed to the Supreme Court, stop pursuing the allegations altogether, especially if they are true?
"Murkowski said she has experienced a "#MeToo" moment, Alaska Public Media reported.
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As the Friday morning vote to advance Kavanaugh's nomination unfurled, the mood inside the Senate chamber was tense.
Amid partisan fights over the confirmation, three women came forward last month to accuse Kavanaugh of sexually assaulting or harassing them during his high school and university years.
Hundreds of protesters against Kavanaugh gathered on the grounds of the Capitol and at the Supreme Court.
But Democrats hope women angered at the Kavanaugh accusations will turn out in large numbers to vote out Republicans.
Inside the Senate, resentments fanned by the battle showed no signs of receding. In the end, there was indeed a two-vote margin, the closest nomination vote since 1881. As senators cast their final votes on Kavanaugh's future, large protests erupted outside.
Christine Blasey Ford testifies to the Senate Judiciary Committee on Capitol Hill in Washington, on September 27, 2018.
Hirono, speaking on ABC's "This Week", said, "I'm focussed like a laser beam on the elections" when asked about impeachment.
Trump also revealed that he believed a widely criticized rally speech in which he mocked Ford's Senate testimony had been a turning point for the nomination, changing the momentum in his favor. "I think that the MS speech had great impact", he said, calling it "a very important thing".
Yet Kavanaugh's path to confirmation seemed unfettered until Ford and two other women emerged with sexual misconduct allegations from the 1980s.
He succeeds Anthony Kennedy, who retired, and is the second judge nominated by Trump to the Supreme Court, giving him an opportunity to put his right-wing seal on the court.