The lawmakers set Tuesday as a deadline for Barr to give up the goods. The House Judiciary Committee plans to vote to authorize subpoenas for the report at a markup hearing Wednesday.
"The allegations at the center of special counsel Mueller's investigation strike at the core of our democracy," the Democrats wrote. "Congress urgently needs his full, unredacted report and its underlying evidence in order to fulfill its constitutional role, including its legislative, appropriations, and oversight responsibilities."
They also want Barr to testify before Nadler's Judiciary Committee — "not in a month, as you have offered, but now." Their topics for Barr will include his initial summary of the principal conclusions from the Mueller report and his decision to "initiate a redaction process that withholds critical information from Congress."
The Democrats also asked Barr not to interfere with Mueller testifying before the Senate Judiciary Committee or other panels after his report is released.
Read the Democrats' letter to barr here.
In addition to Nadler of New York and Schiff of California, the other House committee chairs who made the demand are Ways and Means Chairman Richard Neal of Massachusetts, Financial Services Chairwoman Maxine Waters of California, Oversight and Government Reform Chairman Elijah Cummings of Maryland and Foreign Affairs Chairman Eliot Engel of New York.
The Justice Department declined to comment on the letter to Barr.
Barr, who was confirmed by the Senate in February, has faced mounting criticism from Democrats since he and Deputy Attorney General Rod Rosenstein concluded that Mueller did not find sufficient evidence to merit a charge of obstruction of justice against President Donald Trump.
The attorney general shared that decision, as well as the report's conclusion that the special counsel did not establish collusion between the Trump campaign and Russia, in a four-page summary less than two days after Mueller delivered his long-awaited report.
Barr said he expects to deliver a version of the Mueller report to lawmakers by mid-April, "if not sooner." But Democrats have called on Barr to give them the entire report without any redactions — something Barr has already signaled he will not do.
Barr had recently assured lawmakers that the White House had no plans to exert executive privilege to review the report before it was shared with other parties or the public. Trump said to "just release it," his close ally Sen. Lindsey Graham, R-S.C., told CNN last week.
In a letter sent to Congress on Friday, Barr said the material from the report potentially being redacted includes grand jury-related information, as well as information that could reveal U.S. sources and methods or confidential details about ongoing investigations.
Barr and Republicans have cited federal rules to support their claim that information in the report about grand juries cannot legally be made public. But Democrats have pointed to other high-profile probes involving special investigators, such as those surrounding the Watergate and Monica Lewinsky scandals, in which grand jury information was released to Congress.
"Congress can and has historically been provided with sensitive, unredacted, and classified material that cannot be provided to the general public," the Democrats argued in the letter to Barr.
Mueller spent nearly two years investigating Russia's interference in the 2016 presidential election, as well as possible Trump-campaign collusion and the possible obstruction of justice by Trump himself.
The president, who had long criticized Mueller's probe as a "witch hunt," touted Barr's four-page summary as a "total and complete exoneration" of him and his campaign, even though the report explicitly says it "does not exonerate" Trump on the question of obstruction.
Trump weighed in on Twitter on Tuesday morning, accusing Nadler of hypocrisy and suggesting he and "Shifty Adam Schiff" will never accept the results of Mueller's report.