A practicing Catholic and a member of the Knights of Columbus, Barr said in his confirmation hearings that he did not believe his faith would hinder his ability to serve as an effective attorney general.
Barr appears to have enough support from Republicans, which have a 53-47 advantage in the chamber, to run the Justice Department.
Almost nine in 10 Americans say special counsel Robert Mueller's eventual findings should be made public, according to a new CNN poll released Thursday.
The previous Attorney-General, Jeff Sessions, was sacked by Trump in November.
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"Nothing in existing law or regulation prevents the attorney general from sharing the report", Feinstein said before the vote. Chuck Grassley, an Iowa Republican, and Richard Blumenthal, Connecticut Democrat, introduced legislation requiring a special counsel to submit a report to Congress.
"I have concluded that Mr. Barr is qualified for the position & his record strongly suggests he will exercise independent judgment & uphold the best interests of the DoJ. I hope if he's the next attorney general, and he's likely to be, that what I saw in his family, what I saw in his resume, what I've seen in his commitment to the issue of justice, will come through clearly", Sen.
"I appreciate what Mr. Whitaker has done, but I think it's time for new leadership at the department", Sen. "We are already seeing risky threats to the rule of law".
But he said he could not understand the memo and would vote against Barr's nomination. The Judiciary panel is set to vote on Barr's nomination Tuesday.
Barr was selected after former attorney general Jeff Sessions was pushed out in November 2018. John Kennedy, R-La., said before the vote. Barr, meanwhile, scheduled several individual meetings with lawmakers, seeking to answer whatever outstanding questions they might have had.
Barr said in his hearing last month that he is a friend of Mueller's and that "it is vitally important" that the special counsel be allowed to complete his investigation.