"Besides misapplying the doctrine of executive privilege, since the White House waived these privileges long ago and the (Justice) Department seemed open to sharing these materials with us just yesterday, this decision represents a clear escalation in the Trump administration's blanket defiance of Congress's constitutionally mandated duties," Mr Nadler said.
In an interview with CNN, Mr Nadler said Mr Trump "wants to make himself a king, and Congress cannot permit that".
The White House accused Mr Nadler of a "blatant abuse of power".
Talks with the Justice Department broke down late Tuesday over the committee's subpoena for an unredacted version of Mueller's report.
Mr Nadler said the dispute poses "a constitution crisis" because Mr Trump "is disobeying the law, is refusing all information to Congress."
"We have no choice," Mr Nadler told CNN, but to move forward on the contempt vote.
House Speaker Nancy Pelosi backed the chairman's decision. She suggested Democrats were surprised by the Justice Department's decision to threaten executive privilege to block the release as last-minute talks failed late Tuesday.
"We thought they'd just come back with a counteroffer," she said Wednesday during a Washington Post interview.
Ms Pelosi said if the committee approves contempt resolution, as is expected, the "next step" would be eventual consideration by the full House.
Mr Barr released a redacted version of the Mueller report to the public last month, but Democrats said they want to see the full document, along with underlying evidence, and subpoenaed the full report. The department has rejected that demand, while allowing a handful of politicians to view a version of Mueller's report with fewer redactions. Democrats have said they won't view that version until they get broader access.
The House Judiciary Committee and Justice Department negotiated into the evening Tuesday, trading offers on how many politicians would be able to view the report, how many staff members and whether the department would work with the committee to gain access to secret grand jury material. But those talks ultimately stalled.
In a letter sent late Tuesday, Assistant Attorney-General Stephen Boyd told Mr Nadler that in the face of the committee's contempt vote, Mr Barr would be "compelled to request that the president invoke executive privilege with respect to the materials subject to the subpoena."
It was not immediately clear how such a claim of privilege would work with respect to Mueller's report, which has already been released to the public in redacted form.
Mr Nadler said in response to Mr Boyd's letter to the committee that "this is, of course, not how executive privilege works."
"The Department seemed open to sharing these materials with us earlier today. The Department's legal arguments are without credibility, merit, or legal or factual basis," Mr Nadler said.
The top Republican on the panel, Doug Collins of Georgia, sharply criticised the Democrats' plan to go ahead with the vote.
"I can't imagine a more illogical hill for a legislator to die on," Mr Collins said in a statement.
If the committee holds Mr Barr in contempt, it would be the first step in what could be a protracted, multipronged court battle between Congress and the Trump administration.
Mr Trump has defied requests from House Democrats since the release of Mueller's report last month, and Democrats are fighting the White House on several fronts as they attempt to learn more about the report, call witnesses and obtain Mr Trump's personal and financial documents.
In a related move, Mr Nadler also threatened to hold former White House counsel Don McGahn in contempt of Congress if he doesn't testify before the Judiciary committee later this month. Mr Nadler rejected a White House claim that documents Mr McGahn refused to provide despite a subpoena are controlled by the White House and thus Mr McGahn has no legal right to them.
The Justice Department did not respond to a request for comment on Tuesday's negotiations with Mr Nadler's committee.
On Monday, when the Judiciary panel scheduled the vote, Justice spokeswoman Kerri Kupec said the department has "taken extraordinary steps to accommodate the House Judiciary Committee's requests for information" regarding Mr Mueller's report, but that Mr Nadler had not reciprocated. She noted that Democrats have refused to read the version of Mr Mueller's report with fewer redactions that has been provided to Congress.
A contempt vote against Mr Barr would head to the full House for a vote. If the House were to pass the resolution, it would send a criminal referral to the US lawyer for the District of Columbia, a Justice Department official who is likely to defend the Attorney-General.
Democratic House leaders could also file a lawsuit against the Justice Department to obtain the Mueller report, though the case could take months or even years to resolve. Some committee members have suggested they also could fine Mr Barr as he withholds the information.
Republicans have largely united behind the president, with Senate Majority Leader Mitch McConnell on Tuesday declaring "case closed" on Mueller's Russia probe and potential obstruction by Mr Trump. Mr McConnell said Democrats are "grieving" the result.
Mr Mueller said he could not establish a criminal conspiracy between the Mr Trump campaign and Russia, but he did not reach a conclusion on whether Mr Trump obstructed justice. Mr Mueller didn't charge Mr Trump but wrote that he couldn't exonerate him, either.
Ms Pelosi and Senate Democratic leader Chuck Schumer issued a joint statement calling it "a stunning act of political cynicism and a brazen violation of the oath we all take".
