"I hope - and you have been thus far - be equally forthright in your answers," Feinstein said to Barrett.
But when the senator asked the judge whether she believed that the landmark Roe v. Wade decision -- which protected the right to abortion -- was wrongly decided, Barrett declined to answer.
"Senator, I do want to be forthright and answer every question so far as I can," Barrett said.
"If I express a view on a precedent, one way or another, whether I say I love it or I hate it, it signals to litigants that I might tilt one way or another in a pending case."
Feinstein repeated her question, and Barrett again declined to answer.
The issue of abortion is paramount in the confirmation hearings that could result in a lifetime appointment for the staunchly conservative Barrett and solidify a 6-3 conservative majority on the court.
Republicans have continued to push for abortion bans that might result in overturning the 1973 ruling establishing a woman's right to chose to terminate her pregnancy.