He thanked Kennedy for his service to the nation, and spoke about how he clerked for the justice in 1993.
When Trump ran for the presidency in 2016, he vowed to appoint conservative judges to the Supreme Court, disclosing a list of possible candidates.
That accuser, Julie Swetnick, alleged that at house parties in the early 1980s, she observed Kavanaugh "fondling and grabbing girls without their consent" and, along with others, spiking drinks to force girls to lose their inhibitions.
More recently, Democrats have cast doubt on Kavanaugh's account of his drinking while a teenager, an issue that came up repeatedly during a Senate hearing that included testimony from Kavanaugh and Christine Blasey Ford, who accused him of drunkenly assaulting her while they were in high school. "I mean - they've come to our homes, they've, you know, basically brushed up against members".
"Very, very good", Trump said. "He's a flawless person". Since July of past year, SBA List's field team has reached more than 2 million voters at their homes in key battleground states and will be on the ground every day through Election Day.
Trump also pointed to television footage of protesters outside the Capitol, and said their numbers paled in comparison to the thousands of supporters awaiting him in Kansas. The president's critics say diversity would be undermined if citizenship becomes a census question. 'False charges, false accusations, disgusting statements that were totally untrue, that he knew nothing about'. "Frightful statements that were totally untrue that he knew nothing about".
Ford originally hesitated to put her name to the allegations, telling The Washington Post she feared upending her life while leaving Kavanaugh's Supreme Court confirmation process unaffected. And he toughed it out. She then said her "greatest fears have been realized".
The climactic 50-48 roll call vote on Saturday (local time) on Mr Kavanaugh was the closest vote to confirm a justice since 1881. It capped a fight that seized the national conversation after claims emerged that Kavanaugh had sexually assaulted women three decades ago.
Justice Kavanaugh - who vehemently denies the sexual assault allegations against - is due to take his seat in the Supreme Court on Tuesday to hear arguments about longer prison terms for repeat offenders.
He also singled out Senators Jon Kyl, Lindsey Graham, and Joe Manchin for gratitude.
Kavanaugh was technically sworn in on Saturday evening in a private ceremony at the Supreme Court.
Senate Majority Leader Mitch McConnell, in an interview with Roll Call a month ahead of Election Day, said the contentious debate about the confirmation process was driving up base enthusiasm for the 2018 midterm elections.
"Putting strict constructionists, relatively young, on the courts for lifetime appointments is the best way to have a long-term positive impact on America", McConnell said, "And today is a seminal moment in that effort".