Sen. Orrin Hatch, R-Utah, praised Kavanaugh for hiring female lawyers as his clerks as a judge on the District of Columbia court of appeals, and then posed questions about whether Kavanaugh was aware of sexual harassment allegations against retired circuit court Judge Alex Kozinski in California.
Cruz said his Democratic colleagues were trying to relitigate the results of the 2016 election.
"That's a hypothetical question".
Feinstein later slammed Kavanaugh for ducking the question.
Lee focused most of his questions on the Constitution and separation of powers, asking Kavanaugh at one point to name is his favorite Federalist Paper.
The BBC's Gary O'Donoghue, in Washington, says the investigation into alleged collusion between the Trump campaign and Russian Federation in the 2016 election has raised important constitutional questions about the extent to which an incumbent president can be forced to co-operate.
While this title is undeniably true, it does come with a caveat: Americans have never really expressed a forceful opinion on Supreme Court nominees.
President Clinton was subpoenaed by independent counsel Kenneth Starr in 1998, and eventually agreed to testify voluntarily and the subpoena was withdrawn.
He also declined to say if he thought presidents could pardon themselves.
Kavanaugh's nomination will probably scrape by on a purely party-line vote, both in committee and possibly the full Senate, bearing out that this hearing is everything that has come to define politics in the Trump era. Instead, he said he opposes unlawful regulation. Perabo's no stranger to political activism, and was one of thousands who turned out to protest at Trump Tower in support of the DACA Program which Donald Trump was attempting to close. "That takes some judicial fortitude".
He cited historic cases including the Brown v. Board of Education ruling that desegregated schools and the US v. Nixon decision that compelled the president to turn over the Watergate tapes - a ruling that Kavanaugh had previously questioned.
He also said 70 people in the audience were arrested.
"I understand the importance of the precedent set forth in Roe v Wade", he said. "They will say anything, and are only looking to inflict pain and embarrassment to one of the most highly renowned jurists to ever appear before Congress".
On Wednesday, Durbin challenged Kavanaugh on the grounds that the girl had satisfied all of Texas's prerequisites to obtaining an abortion, including an ultrasound and securing a judicial bypass to parental consent requirements.
The judge's work in the George W. Bush White House also has figured in the hearing, particularly as Democratic senators have fought for greater access to his emails and other documents during his three years as staff secretary.
Democrats are keen to push Mr Kavanaugh on the issue, he adds.
According to Fox News, Capitol Police have arrested around two dozen protestors who were disrupting the hearing and others were escorted out of the room.
That would allow Senate majority leader Mitch McConnell, Republican of Kentucky, to tee up votes on the floor confirming Kavanaugh during the last week of September.
The huge stakes and fierce passions aroused by the lifetime appointment were on display this week as shouts of protests and Democratic demands for a postponement greeted the start of his Senate confirmation hearing.
In her remarks, Klobuchar suggested that 1) aspects of the Trump presidency to date have left her anxious that Trump's willingness to abide by laws and precedents; 2) that Kavanaugh's position on the three-judge panel left her anxious that as a Supreme Court justice he might take an extremely expansive view of presidential power and 3) that that might be among the reasons Trump wants him on the Supreme Court. At age 53, Kavanaugh could serve on the court for decades.
Republicans hope to confirm Kavanaugh by October 1, the first day of the Supreme Court's new term.