"I want to apologize to Brett and the entire Kavanaugh family for the terrible pain and suffering you have been forced to endure," Trump said.
Kavanaugh, in his speech, thanked Trump for his "unwavering support" and said he was not bitter about the combative process.
"The Senate confirmation process was contentious and emotional. That process is over. My focus now is to be the best justice I can be. I take this office with gratitude. And no bitterness," Kavanaugh said.
“Every American can be assured I’ll be an impartial justice,” he said.
Kavanaugh was officially sworn in as the 114th Supreme Court justice by retired Justice Anthony Kennedy on Saturday in a private ceremony attended by his wife and two daughters shortly after the Senate vote.
Kavanaugh fills the seat vacated by Anthony Kennedy when he retired from the high court in June.
Kavanaugh's confirmation came amid allegations of sexual assault by three women, one of whom, Christine Blasey Ford, testified during a Senate hearing that she was 100 percent sure that it was Kavanaugh who assaulted her at a party when they were both teenagers.
Kavanaugh vehemently denied the accusations.