The US president said that Mr Kavanaugh was an “outstanding person” as he arrived in New York to attend the United Nations General Assembly and responded to the new claim.
Mr Trump said: “For people to come out of the woodwork from 36 years ago, and 30 years ago and never mention it - all of a sudden it happens. In my opinion it's totally political. It's totally political."
The defence came after The New Yorker magazine published an accusation by a woman who attended Yale University with Mr Kavanaugh.
The magazine says Senate Democrats, who brought to light the claims of Christine Blasey Ford against President Donald Trump’s pick for the nation’s top court, are investigating an incident reported by Deborah Ramirez, 53, a former Yale student.
Mr Kavanaugh denied the allegation, and the White House issued a statement saying it stands firmly behind his nomination.
The claim dates to the 1983-84 academic school year, when Mr Kavanaugh was a freshman at Yale, the New Yorker reported. Ramirez said Mr Kavanaugh exposed himself to her during a drunken dormitory party.
The offices of at least four Democratic senators have received information about Ramirez’s allegation, the New Yorker reported.
Mrs Ford and Mr Kavanaugh are scheduled to testify before a Senate panel on Thursday about what she says was a sexual assault by him at a party when they were teenagers.
Mr Kavanaugh said in the statement about the latest claim that “this alleged event from 35 years ago did not happen. The people who me then know that this did not happen, and have said so. This is a smear, plain and simple.”
Separately, Michael Avenatti, the lawyer best known for representing adult film star Stephanie Clifford, said on Twitter that he represents a woman “with credible information regarding Judge Kavanaugh.” His client is not Ramirez, Mr Avenatti tweeted.
I represent a woman with credible information regarding Judge Kavanaugh and Mark Judge. We will be demanding the opportunity to present testimony to the committee and will likewise be demanding that Judge and others be subpoenaed to testify. The nomination must be withdrawn.— Michael Avenatti (@MichaelAvenatti) September 23, 2018
“This 35-year-old, uncorroborated claim is the latest in a coordinated smear campaign by the Democrats designed to tear down a good man,” White House spokeswoman Kerri Kupec said in a statement.
“This claim is denied by all who were said to be present and is wholly inconsistent with what many women and men who knew Judge Kavanaugh at the time in college say.”