In a series of tweets, Mr Trump accused Democrats and the news media of working to intimidate Mr Kavanaugh with the new allegation, which comes less than a year after similar claims were made during his Senate confirmation hearings.
The new allegation, in which Mr Kavanaugh was said to have exposed himself to a female Yale classmate before others pushed his genitals into the hands of the woman, has led some to call for the justice's impeachment.
"Brett Kavanaugh should start suing people for liable, or the Justice Department should come to his rescue. The lies being told about him are unbelievable. False Accusations without recrimination. When does it stop? They are trying to influence his opinions. Can’t let that happen!" Mr Trump wrote.
In an earlier tweet, Mr Trump said: "Now the Radical Left Democrats and their Partner, the LameStream Media, are after Brett Kavanaugh again, talking loudly of their favorite word, impeachment. He is an innocent man who has been treated HORRIBLY. Such lies about him. They want to scare him into turning Liberal!"