Still, Democrats senator Chris Coons said he believed it would be premature for his party to talk about re-investigating Mr Kavanaugh or a possible impeachment if it takes control of the chamber, stressing a need to help heal the country.
He told an audience that included the entire Supreme Court and a Who´s Who of Republican movers and shakers that he had "no bitterness" and would never bring politics into the top court.
Trump's first Supreme Court appointee, Neil Gorsuch, also took part in a White House oath ceremony. Court watchers will be looking to see whether the new justice asks questions at arguments and, if so, what he asks.
Kavanaugh will be closely scrutinized from his first day on the bench.
Susan Collins of ME was among the senators who new Justice Brett Kavanaugh singled out for "special gratitude" Monday evening during his ceremonial swearing in to the Supreme Court at the White House.
"I think a lot of Democrats are going to vote Republican", he said in his earlier comments outside the White House.
He said all four of the clerks who will work for him at the high court are women. But Kavanaugh's confirmation was delayed as the Senate considered allegations that he had sexually assaulted a woman in high school.
Trump has now put his stamp on the court with his second justice in as many years.
Haley Announces Resignation, Will Serve Until Year's End
Israel's United Nations ambassador, Danny Danon, in a statement praised the outgoing ambassador: "Thank you, Nikki Haley! ". Echoing previous statements from Trump, Haley said the United States under his presidency is now respected around the world.
Kavanaugh took his seat at the right end of the courtroom's mahogany bench - the location assigned to the court's junior-most member - and wore traditional black robes like the other justices.
Even though he was already sworn in, a swearing-in ceremony for Kavanaugh is set for 7 p.m. on Monday at the White House, prolonging a victory lap for Trump.
Nadler called the FBI investigation into the allegations against Kavanaugh - which only lasted a week and was limited in scope - a "whitewash" investigation, according to the New York Times.
Trump on Twitter on Tuesday said he was "very proud" of Kavanaugh and his family, and disparaged the anti-Kavanaugh protesters. By the way, given the volume and shrillness of anti-Kavanaugh protests - from his original hearings all the way through to his delayed confirmation - this is an interesting detail, isn't it?
Kavanaugh said he would aim to be a force for stability and unity on the court, whose other eight members all attended the ceremony.
Roberts prompted laughter when he described asking his law clerks to try to grab a dollar bill from his hand to determine if that constituted a violent act. On Wednesday, the only other day of arguments this week, the court will hear another two hours of arguments.
Kavanaugh posed questions to lawyers in both cases before the court, his first one coming about 20 minutes into the arguments.
Although he missed the court's first week, none of the six cases argued dealt with blockbuster issues. Kavanaugh won't vote in those cases, but if the court is split 4-4, it could decide to have those cases reargued so Kavanaugh can break the tie. He'll also be the one to answer the door at those meetings if someone knocks to deliver something such as a justice's coffee or forgotten glasses.