Donald Trump apologised "on behalf of the nation" to newly confirmed Supreme Court Justice Brett Kavanaugh, and said the judge had been "proven innocent" of sexual assault allegations.

In a swearing-in ceremony at the White House, following a torrid confirmation process that divided America, the US president slammed Democrat opponents for having waged a "campaign of personal destruction" against Justice Kavanaugh.

The new Supreme Court justice himself sought to leave the controversy behind, promising to be a "team player" on the nine-member court, and a "great justice for all Americans".

Justice Kavanaugh, who will be a conservative voice on the court, said he had "no bitterness," that he felt "gratitude" for eventually being confirmed, and that the Supreme Court was "not a partisan or political institution".

At the ceremony in the East Room of the White House, Justice Kavanaugh’s wife Ashley held the Bible as he took the oath, and his two daughters stood by his side.

Justice Anthony Kennedy, the retiring judge whose place he is taking, administered the oath in front of the eight other serving members of the Supreme Court.