The names were organized and posted online Monday by an anti-Trump nonprofit organization called "Protect Democracy".
Barr has released a redacted version of Special Counsel Robert Mueller's report on his investigation into Russian interference in the 2016 US presidential election. He ultimately reached no conclusion on whether Trump had criminally obstructed justice, citing in part an opinion from the department's Office of Legal Counsel that says a sitting president can not be indicted.
Attorney General William Barr, who criticized the obstruction probe a year ago, said after the conclusion of Mueller's investigation that both he and Deputy Attorney General Rod Rosenstein determined Mueller's evidence was "not sufficient" to support prosecuting Trump for obstruction.
Mueller's team, though, wrote that it decided not to make a "traditional prosecutorial judgment" in part because of the Justice Department opinion on not indicting sitting presidents and because the evidence obtained "presents hard issues that would need to be resolved" if they were to do so.
"'No redos for the Dems!'" The House Judiciary Committee is seeking to have Mueller testify on May 15.
As the fight with Barr has escalated, Democrats have been in negotiations to hear from Mueller himself.
As of Monday afternoon, the statement had 379 signatories.
Trump Directs Officials to Toughen Asylum Rules
Speaking to reporters, they did not say a word about Trump's asylum memorandum or any other aspect of his anti-immigrant policy. The current backlog of cases totals over 800,000, with an average wait time of nearly two years.
Such a move against an attorney general is not unprecedented, however.
Barr has said the OLC opinion played no role in his conclusion, and Trump has used the attorney general's finding to claim that the report found no obstruction.
"Bob Mueller should not testify", he tweeted.
"There was no crime, except on the other side (incredibly not covered in the Report), and NO OBSTRUCTION", President Trump tweeted on Sunday.
House Judiciary Chairman Jerry Nadler said last week that May 15 was the committee's target date for Mueller to testify, but it has not yet been finalized.
Barr had objected to Democrats' plans to use outside attorneys to conduct part of the questioning; Democrats say this has been done before, notably in the Watergate hearings.
Peter Carr, a spokesman for Mueller, declined to comment on Sunday. He added, "The White House has so far indicated they would not interfere with Mr. Mueller's attempts to testify".
The heart of the dispute is over the grand jury material in the Mueller report, which Nadler has said Congress is entitled to but Barr argues he's not legally allowed to provide without a court order. Sections of the publicly-released version of Mueller's report detailing the actions of Russia's "Internet Research Agency" (IRA) and other Russian hacking operations "contain significant redactions, which impair the ability of the Committee to gain a complete understanding of Russia's actions", the contempt report states.