Another woman came forward over the weekend, telling The New Yorker magazine that Kavanaugh exposed himself and caused her to touch his penis at a party when both were Yale freshmen.
Feinstein's office said it had no idea who leaked the letter.
Asked how she could be so sure it was Kavanaugh who attacked her, Blasey Ford responded with confidence: "The same way that I'm sure that I'm talking to you right now".
Rep. Anna Eshoo represents California's 18th congressional district and was the first member of Congress to hear Ford's story.
She said she was terrified to come forward but did so because she felt it was her civic duty. Senator Mazie Hirono of Hawaii hit out at Mitchell's approach during the hearing, saying she had aimed to undermine Ford's credibility.
At a news conference in NY a day before Kavanaugh was set to testify before the Senate Judiciary Committee, Trump pledged to listen to the testimony of Kavanaugh's accuser and even said he was open to changing his mind about his nominee.More news: Apple buys music app Shazam
Before the Senate hearing on Thursday, Ford had never appeared on camera, and was only depicted in news media reports with a grainy photo lifted from the internet.
Blasey Ford testified that Kavanaugh and his friend Mark Judge, both "visibly drunk", pushed her into an upstairs room at the party and locked the door.
United States president Donald Trump has acknowledged that past accusations of sexual misconduct against him have influenced the way he views similar allegations against other men, including his Supreme Court nominee.
"You may defeat me in the final vote, but you'll never get me to quit, never", he said.
"Indelible in the hippocampus is the laughter", said Ford, who is a research psychologist and professor at Palo Alto University.
"I am innocent of this charge", Kavanaugh says. All sexual assault victims should be able to decide for themselves whether their private experience is made public'.More news: US will not tap oil reserve as Iran sanctions loom: Perry
Kavanaugh also allegedly put his hand over Ford's mouth so she could not scream. She said at the beginning of her testimony, when asked if she would need a break after her opening remarks, that she might need some coffee.
Over the past few days, other false and uncorroborated accusations have been aired.
Senators who don't trust or much like each other will be charged with settling a vicious debate - with President Donald Trump hardly a bystander, or a predictable force.
"There are millions of victims and survivors out there who have been inspired by your courage-I am", said Leahy.
However, that is going to require facing questions the nation has been reluctant to address, including the prevalence of the problem and the fact that abusers don't always look like stereotypical monsters, she said. "We'll wait to see if she gets that invitation and we'll go from there".More news: Brett Kavanaugh Refuses To Say Whether He'd Want Mark Judge To Testify