Attorneys representing Christine Blasey Ford, who accused Kavanaugh of sexual assault at a party 36 years ago, had sent a letter to Senate judiciary committee Chairman Chuck Grassley asking for the FBI inquiry.
The attorneys argued the investigation is necessary for the committee to be "fully informed before conducting any hearing or making any decisions."
Ford has faced "vicious harassment and even death threats," since going public with allegations, the attorneys said.
Grassley, though, declined the delay request.
"The invitation for Monday still stands," Grassley said. "Nothing the FBI or any other investigator does would have any bearing on what Dr. Ford tells the committee, so there is no reason for any further delay."
Kavanaugh has denied he assaulted anyone.
"I am willing to talk to the Senate judiciary committee in any way the committee deems appropriate to refute this false allegation, from 36 years ago, and defend my integrity," he said Tuesday.
A lawyer of Patrick Smyth, a former classmate of Kavanaugh at Georgetown Prep, an all-boys school in North Bethesda, Md., sent a letter to the Senate Judiciary Committee, saying that Smyth believes he is a person named "PJ" that Ford has alleged was present at the party.
"I understand that I have been identified by Dr. Christine Blasey Ford as the person she remembers as 'PJ' who supposedly was present at the party she described in her statements to the Washington Post," Smyth says in his statement to the Senate Judiciary Committee. "I am issuing this statement today to make it clear to all involved that I have no knowledge of the party in question; nor do I have any knowledge of the allegations of improper conduct she has leveled against Brett Kavanaugh."
Democrats like Senate Minority Leader Chuck Schumer support postponing the hearing for an investigation.
"I strongly support Dr. Ford's call for an FBI investigation before a hearing is held," Schumer said. "Dr. Ford's call for the FBI to investigate also demonstrates her confidence that when all the facts are examined by an impartial investigation, her account will be further corroborated and confirmed."
"Asking her to come forward in four or five days and sit before the Judiciary Committee on national TV is not a fair process," Banks said. "If they care about doing the right thing here and treating this seriously as they have said, then they will do the right thing and they will properly investigate this, and she will work with them in that investigation and also to share her story with the committee."
Ford accused Kavanaugh in a Washington Post article, in which she said she was sexually assaulted by Kavanugh in the 1980s when they were high school students in Maryland.
She said she didn't tell anyone any details about the ordeal until a therapy session in 2012.
The accusations have delayed a Senate vote on Kavanaugh's nomination.