"Our progress is such that I anticipate we will be in a position to release the report by mid-April, if not sooner", Barr wrote in a letter to House Judiciary Committee Chairman Jerrold Nadler, Democrat of NY, and Senate Judiciary Committee Chairman Lindsey Graham, Republican of SC.
Barr also offered to testify shortly after the report is released, suggesting May 1 for the Senate committee and May 2 for the House committee.
Democrats have been intensifying their demands for Robert Mueller's full report after learning the special counsel's findings from his Trump-Russia investigation run to more than 300 pages. Barr said he and Deputy Attorney General Rod Rosenstein decided on their own that Mueller's evidence was insufficient to establish that the president committed obstruction.
A fight has continued between Democrats and Republicans over the public release of the report, with Democrats having repeatedly called in Congress for Mr Barr to quickly release the full findings.
Barr said in a letter to Nadler and other lawmakers Friday that he would send the report to Congress "by mid-April, if not sooner". He added that there are no plans to submit the report to the White House for a privilege review.
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Asked about the report's conclusions a day after they were released, the president said there was "a lot of people out there that have done some very, very evil things, very bad things, I would say treasonous things, against our country".
Barr's letter aimed to reassure lawmakers and the public that the process for handling the report - which numbers almost 400 pages, he said - would be aboveboard and fair.
Jennifer Rubin, a columnist for the Washington Post, also accused Barr of a coverup, writing that the AG would "defeat the entire goal of a special counsel by weighing in to exonerate the president of any wrongdoing and to provide a scant summary of hundreds of pages of evidence".
The White House has been taking a prolonged victory lap after receiving Robert Mueller's inconclusive report.
Barr further confirmed that the Justice Department and Muller's team were working to redact four types of information from the report: grand jury material, sensitive intelligence material, information that involves ongoing investigations, and "information that would unduly infringe on the personal privacy and reputational interests of peripheral third parties".
While the Mueller probe is officially completed, he referred some matters he discovered to USA attorneys' offices. Lindsey Graham and Rep. Jerrold Nadler, the chairmen of the Senate and House Judiciary Committees.
"There is ample precedent for the Department of Justice sharing all of the information that the Attorney General proposes to redact to the appropriate congressional committees", Nadler said in a statement.