Barbara Van Gelder, Judge's lawyer, confirmed the interview had been completed but declined to say exactly when it ended or what Judge was asked.
In testimony last Thursday, Ford described attending a house party in the Washington DC suburbs in the early 1980s at which she was pushed into a bedroom where a drunken Kavanaugh held her down, groped her, tried to strip her and left her fearing for her life.
Mr Kavanaugh has vehemently denied the allegations.
Attorneys for Christine Blasey Ford, who says she was sexually assaulted by Kavanaugh at a party when they were teenagers, wrote a letter to FBI Director Christopher Wray asking why the FBI hasn't contacted their client after she offered to cooperate in the FBI's reopened background investigation of Kavanaugh.
President Trump said that if Kavanaugh did lie to Congress, then "that would not be acceptable", but the White House has said the administration does not feel that Kavanaugh lied under oath. If every Democrat votes no, Republicans can lose only one R vote and still confirm Kavanaugh.
Republicans have a narrow 51-49 majority in the Senate and Trump and party leaders want to get Kavanaugh confirmed ahead of November 6 elections, in which Democrats are trying to seize control of Congress.
Michael R. Bromwich, a lawyer for Blasey Ford, called Trump's comments a "vicious, vile and soulless attack" on her.
GOP Sens. Lisa Murkowski and Jeff Flake are the other key senators.
McConnell said that Democrats continue to try to "move the goal posts" on Kavanaugh's confirmation and predicted they would be unsatisfied when the Federal Bureau of Investigation completes its work this week.
Mr Kavanaugh denies the claims. The Kavanaugh hearing crystallized what has become a central divide in American politics.
He also mocked Democrats as acting "holier than thou" and focused on several potential 2020 contenders by name, including former Vice President Joe Biden, Sen.
The president said: "It's a very scary time for young men in America when you can be guilty of something that you may not be guilty of".
Sen. Susan Collins, R-Maine, considered a swing vote on the nomination, refused to be drawn into the issue of Kavanaugh's credibility or the timing of an eventual vote on Tuesday.
Democrats have seized most recently on Kavanaugh's indignant, emotional testimony before the Judiciary Committee to question whether he has the temperament for a lifetime appointment on the nation's highest court. "If we took 10 years, they'd want more time", he groused. "There's plenty to disbelieve in what he said but, again, it's very hard to sort through this until you have the investigation, which is why we pushed so hard to make sure that took place".
Judge, a conservative writer, was a friend and classmate of Kavanaugh's at Georgetown Preparatory School, a private, all-male Catholic school in North Bethesda, Maryland. "I don't remember. How'd you get there?" Trump spoke about his brother's troubles in October 2017 and suggested that his brother had "a very, very, very tough life because of alcohol" and "I learned because of Fred".
"I'm not going to do a hypothetical, I really want to go with facts and that's why I pressed for a supplemental FBI investigation", she told reporters. Kavanaugh could be sitting on the Supreme Court in January, when the course was scheduled. Senate Republicans have privately expressed similar sentiments. A third woman who has accused the judge of sexual misconduct in the 1980s, Julie Swetnick, was not on the initial list of witnesses to be interviewed.
Starting on Tuesday, scores of protesters also planned to deliver morning cups of coffee to Senate offices with messages from victims of sexual assault to encourage them to "wake up to the truth", the Center for Popular Democracy advocacy group said.