Sheldon Whitehouse (R.I.), and Mazie Hirono - left after committee chairman Chuck Grassley (R-Iowa) began speaking ahead of a hearing to decide whether Kavanaugh, accused of sexual assault while in high school by Christine Blasey Ford, should receive a nomination.
"I swear today, under oath, before the Senate and the nation, before my family and God, I am innocent of this charge", Kavanaugh told the Judiciary Committee.
"I am not going to make a predetermination without hearing from Dr. Ford, who has come forward, and also from hearing from Judge Kavanaugh himself".
A third woman, Julie Swetnick, has also accused Kavanaugh of sexual misconduct. Neither has said whether she would vote to confirm Kavanaugh.
Republicans are concerned, among other reasons, that further investigations could push a vote past the November elections that may switch Senate control back to the Democrats and make consideration of any Trump nominee more hard.
As the Republicans have a slim 11-10 majority on the committee, Flake's support is likely to tip the vote in favour of Mr Kavanaugh.
Some experts say Ford's use of scientific brain function has helped lend to her credibility. "That's what happened to me, and that's what you're telling all women in America".
Democrats have rallied strongly behind Ms Ford.
Zoe Chance, a marketing professor at Yale School of Management, said that in terms of winning over public opinion, Ford and Kavanaugh "are both doing the right thing". She added that the test took place on either the same day or near the date of her grandmother's funeral.
"She didn't seem in it for gain", said Pierman, who lives in the suburbs of Cleveland. The American Bar Association, which earlier endorsed Kavanaugh, and the dean of Yale Law School, which Kavanaugh attended, also called for an Federal Bureau of Investigation probe, the first indication of the legal profession turning on the nominee.
Later, she told Senator Dick Durbin that her certainty was "100%".
The all-male Republican contingent on the committee brought in a female prosecutor, Rachel Mitchell, to ask questions of Prof.
He said the judge was entitled to the "presumption of innocence. absent corroborating evidence". Blasey Ford said she was able to break free and flee the house. "Two friends having a really good time with one another", she replied. Jeff Flake of Arizona, a member of the committee, announced he would vote to confirm Kavanaugh. "He embodied the anger so many sexual assault victims fear; the anger that keeps so many of us from coming forward".
He also expressed frustrations with the delays in the process guided by Republicans and took a shot at lawyer Michael Avenatti, who is representing the latest accuser.
Some Democrats have called on Kavanaugh to withdraw in light of the allegations.
In July, Baker, Hogan and Scott were the lone Republican governors to not sign a letter to Senate leaders offering support for Kavanaugh's nomination.
In a later instance at the hearing, Ford was asked what she remembered most about the alleged assault, in which she used brain function to again describe her memory.
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