Barr will testify today before the Senate Appropriations Committee.
That letter said that Mr Mueller did not find a criminal conspiracy between Russian Federation and Mr Trump's associates, and that Mr Barr did not believe the evidence in the report was sufficient to prove the president had obstructed justice.
Barr's statement Wednesday that he expected to release a redacted version of Mueller's almost 400-page report next week marked a slight change from the estimate he gave Tuesday, when he said the release would be within a week.
Rep. Nita Lowey (D- N.Y.), chair of the appropriations committee, described Barr's handling of the matter as "unacceptable" and accused him of "cherry picking" Mueller's findings "to draw the most favorable conclusion possible for the president". Barr and Deputy Attorney General Rod Rosenstein concluded the evidence Mueller presented did not amount to an obstruction charge.
The top Republican on the House Intelligence Committee, California Rep. Devin Nunes, told Fox News on Sunday that he was sending eight criminal referrals to the Justice Department, apparently linked to investigations he started in the last Congress about the beginnings of the Russian Federation probe. That FBI investigation began in July 2016 and eventually included surveillance warrants targeting Carter Page, a former Trump campaign advisor.
"If this is a 400-page report.to send us a four-page summary that just talks about the high-level conclusions is potentially misleading", Coons said. Rep. Jerrold Nadler, a New York Democrat and chairman of the House judiciary panel, confirmed the May 2 date on Twitter and said he would like Mueller to testify.
Barr said in the summary released last month that Mueller didn't find a criminal conspiracy between the campaign and the Kremlin. "We look forward to hearing from Mr. Mueller at the appropriate time".
Senate Judiciary Committee Chairman Lindsey Graham, R-S.C., has said he would be satisfied hearing only from Barr and not Mueller.
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EPIC filed a lawsuit on March 22 demanding the release of the Mueller report, arguing that the public has the right to know the full scope of Russia's interference in the 2016 election.
Trump seems to be of the same mind.
Trump has said he will not use a legal doctrine called executive privilege, which allows a president to withhold information about internal executive branch deliberations from other branches of government, to block portions of the report. "It will never end, but that's the way life goes!" he tweeted Monday.
Barr said that the White House had not reviewed in advance his communications to Congress about the report, but he rebuffed Lowey's attempt to ask whether the White House had seen the report since he sent his summary letter. Everyone will soon be able to read it on their own. Jeanne Shaheen if he believed spying on the campaign occurred, Barr said, "Yes I think spying did occur".
The chairman of the Ways and Means subcommittee, Democratic representative Jose Serrano of NY, told Mr Barr there were "serious concerns about the process by which you formulated your letter; and uncertainty about when we can expect to see the full report".
The testimony focused on the Justice Department's proposed $29.2-billion budget and its efforts to combat violent crime, opioids and immigration violations.
The impending release of the 400-page report is expected to shed light on some of the more contentious episodes of Trump's election bid and presidency, including his firing of Federal Bureau of Investigation head James Comey in 2017 and his campaign's contacts with Russians.