Hasen said the full report might open up some big questions about the attorney general and his actions after receiving Mueller's findings.
"To deny the Judiciary Committee and the Congress the knowledge of what's in parts of the Mueller report is not proper", Nadler said.
Deputy Attorney General Rod Rosenstein pushed back Thursday against allegations that Attorney General William Barr had been biased in his handling of Special Counsel Robert Mueller's final report, calling such accusations "bizarre".
Barr has suggested there may have been "improper surveillance" on President Trump's 2016 campaign and said he was "looking into it".
Last month, Barr released a summary of Mueller's findings, almost 48 hours after the special counsel's investigation was completed.More news: Antisemitism is threat to Labour at the ballot box, says inquiry head
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Rosenstein appointed Mueller as special counsel for the Russian Federation probe in May 2017, after Trump fired former FBI director James Comey, who had directed the investigation to that point.
Since the release of Barr's summary, Trump has claimed "total exoneration, no collusion, no obstruction".
Last month, Barr released a letter saying Mueller had not established evidence of collusion between the Trump campaign and Russian operatives, but also saying Mueller had provided evidence of alleged obstruction of justice by Donald Trump while declining to recommend prosecution. He was referring to Hillary Clinton, his 2016 opponent, and the Democratic National Committee, which supported her candidacy. The main questions that aides want to be able to answer for Trump: why Mueller couldn't conclude whether Trump obstructed justice and what he meant when he said "much" of Trump's conduct was public.