The sharp exchanges on the Senate floor came one day after Kavanaugh appeared on USA cable television - an unprecedented move for a Supreme Court nominee - to refute all allegations of sexual misconduct.
Speaking at the United Nations General Assembly in NY, the USA president showered his controversial pick for the job with praise and accused Democrats of running a "con game" against him. Dr. Christine Blasey Ford, a California psychology professor, says he assaulted her years ago at a suburban Maryland high school party.
"This is a con game being played by the Democrats", the President said during a photo op with the President of Colombia, urging the Senate to confirm Kavanaugh to the Supreme Court.
"This is a high quality person and it would be a terrible insult to our country" if he's not confirmed.
"There's a chance that this could be one of the single-most unfair, unjust things to happen to a candidate for anything", Trump said following a meeting Monday afternoon at the United Nations.
Ramirez told her story in a piece published in the New Yorker over the weekend.
"I'm not going to let false accusations drive us out of this process", he added, repeatedly calling for a "fair process". Kavanaugh has denied both allegations.
Mr Kavanaugh said it was possible he may have met Ms Ford at some time, but he said they were not friends and did not travel in the same social circles.
The Kavanaugh confirmation fight comes just weeks before November 6 congressional elections in which Democrats are trying to take control of Congress from Republicans, against a backdrop of the #MeToo movement fighting sexual harassment and assault.
On Thursday, Judge Kavanaugh and another accuser from his high school years testify before a US Senate panel.
Republicans made a decision to hire a female attorney because of the risk that the panel's 11 Republican men - there are no GOP women on the committee - might say something insensitive to Ford.
He called the allegations "grotesque and obvious character assassination" and says they could dissuade others from entering public service. Yet there remained concern among aides, and Trump himself, as to how Kavanaugh, who appeared shaken at times during the interview, would hold up facing far fiercer questioning from Senate Democrats on Thursday, according to a White House official not authorized to speak publicly about private conversations. Brett Kavanaugh is an absolutely outstanding person.
"I was not at the party described", Mr Kavanaugh said.
Trump and Republican leaders are accusing Democrats of a smear campaign by using accusations by two women of sexual misconduct by Kavanaugh in the 1980s to try scuttling his Senate confirmation. Trump's first nominee, Judge Gorsuch, was confirmed by the Senate on April 7, 2017.