Judge Brett Kavanaugh on the third day of his Senate confirmation hearings dodged questions about whether he would recuse himself from cases related to the special counsel Robert Mueller or the Russia investigation if they reach the Supreme Court.

Sen. Cory Booker of New Jersey posed the question on Thursday, asking Kavanaugh to dispel suspicions that President Donald Trump could have had the Russia probe in mind when he nominated Kavanaugh to the nation's high court.

"Even at the jeopardy of President Trump pulling back your nomination, why not now alleviate all of that suspicion that a reasonable person can have?" Booker asked.

Kavanaugh said he would not answer because, in his view, it would jeopardize the independence of the judiciary.

The line of questioning follows that of other Democratic senators this week who have sought clarity about Kavanaugh's political leanings.

Democratic senators kept the heat on Judge Brett Kavanaugh on the third day of his Senate confirmation hearings, asking pointed questions about his leanings on women's rights, racial profiling, and the potential role he could play if a case related to the Russia investigation reaches the Supreme Court.

Sen. Cory Booker of New Jersey asked Kavanaugh whether he would recuse himself from a case involving the special counsel Robert Mueller or the Russia probe if the nation's high court takes up the matter.

The issue has been on the minds of Democratic senators who have expressed concerns about Kavanaugh's views on executive branch powers. The Supreme Court could weigh in on a number of potential scenarios that could play out in the Russia probe or the obstruction of justice case involving Trump in the near term.

"Even at the jeopardy of President Trump pulling back your nomination, why not now alleviate all of that suspicion that a reasonable person might have?" Booker asked Kavanaugh.

Kavanaugh chose not to take a position on recusal because, in his view, making such a decision beforehand would jeopardize the impartiality of the court.

Notably, the US attorney general Jeff Sessions recused himself from the Russia probe in March 2017, citing his previous contacts with Russian officials during the 2016 election.

Kavanaugh demurred on the issue: "If I committed to deciding a particular case ... all I would be doing is demonstrating that I don't have the independence of the judiciary. That is necessary to be a good judge."

The Supreme Court nominee had a similar response to California Sen. Kamala Harris, who asked him on Thursday to address concerns about his ability to remain impartial in judicial matters related to Trump. To that, Kavanaugh insisted that his record as a judge speaks for him.

"My independence, I believe, has been demonstrated by my 12-year record," Kavanaugh said. He repeated that he firmly adheres to those principles.

When Harris took up the recusal question Sen. Booker asked previously, Kavanaugh said, "the independence of the judiciary requires that I not commit" to participating or not participating in a case.

Harris and Kavanaugh crossed swords one day earlier when she cornered him on a question about whether he had spoken about the Russia probe or Mueller with anyone at the law firm of Trump's personal lawyer, Marc Kasowitz.

Watch a portion of the Booker-Kavanaugh exchange below: