The president's rendering of a verdict on the sexual assault allegations risks further antagonizing political opponents at a moment that the "Me Too" movement demands accountability for sexual misconduct.
She said that the disruptions during the hearing and Supreme Court protests were "not what we want for our country".
Kavanaugh took the two required oaths privately at the court on Saturday, letting him begin work right away.
Before hearing arguments on October 9, the justices turned aside appeals of a 2017 ruling authored by Kavanaugh on the lower court that struck down a 2015 environmental rule imposed under Democratic former President Barack Obama.
Kavanaugh thanked some of the senators key to his confirmation, including Maine Republican Susan Collins and West Virginia Democrat Joe Manchin, who sealed the bare majority needed to confirm him. Fifty-six percent are angry about how the Senate treated Christine Blasey Ford, the woman who accused Kavanaugh of sexual assault, including 35 percent who are very angry, Rasmussen said.
But while Kavanaugh gained ground with the Republican base, he lost it with the broader public, as 51 percent of voters say the Senate should have rejected his Supreme Court bid. And while they should be looked at in the broader scope of things, they suggest the building narrative that the Kavanaugh confirmation was a disaster for Democrats isn't totally correct.
He said, "I'm just reminding you what the history has been".More news: Bulgarian journalist reporting on corruption found murdered
Kavanaugh's wife watched the lively session as did his daughters, who were granted a day off from school to see their father's first day on the nation's top court.
Republicans had hoped to confirm Kavanaugh in time for him to join the court on October 1, the start of the new term. He had already hired four law clerks, all women.
Kavanaugh was sworn in Saturday evening in a private ceremony as protesters chanted outside the court building. He denied the allegations.
"I say that it's a very scary time for young men in America, when you can be guilty of something that you may not be guilty of".
This "speaking truth to power" line has been spoken in reference to Anita Hill, the woman who accused SCOTUS Justice Clarence Thomas of sexual harassment back in 1991; Hill has now had an HBO movie and a documentary glorify her testimony.
Ultimately, Kavanaugh was confirmed by a vote of 50-48.
"What happened to the Kavanaugh family violates every notion of fairness, decency and due process", the President continued.
Kavanaugh's first Supreme Court case involved arguments over the federal criminal sentencing law and came hours after Trump staged a ceremonial swearing-in for Kavanaugh at the White House.