Mueller, who is investigating any collusion with the Russians on the part of President Trump and his campaign associates, reportedly may be close to wrapping up the almost two-year probe.
"After taking almost two years, costing tens of millions of taxpayer dollars, and providing limited public information about its scope, I am especially concerned about what would happen if the report was not made available to Congress", Scalise said in a statement.
The President has repeatedly railed against the investigation, denouncing it as a witch hunt and insisting there was no collusion between associates of his presidential campaign and Russian Federation. Four Republicans voted present. He also met with Associated Press reporters on April 11, 2017 to discuss a case against Manafort.
The non-binding resolution, offered by House Judiciary Chairman Jerrold Nadler and several other Democratic chairs, passed 420-0 on Thursday.
The top Republican on the House Judiciary panel, Georgia Rep. Doug Collins, voted for the resolution but said it was unnecessary.
Manafort's sentencing hearing underway in DC
Last week after Manafort was sentenced in Virginia, Trump said he feels "very badly" for his former campaign chairman. Manafort was also ordered to pay $24 million in restitution and a $50,000 fine.
But Democrats have said they are unsatisfied with Barr's answers and want a stronger commitment to releasing the full report, along with interview transcripts and other underlying evidence.
Under the regulation governing Mr. Mueller's work, he must submit a report at the conclusion of his investigation to the USA attorney general explaining his decisions to pursue or decline prosecutions, including explanations of cases he investigated but he decided not to bring charges.
Though they voted for the resolution, many Republicans expressed skepticism about the wisdom and likely success of Democrats' quest.
Barr said at his January confirmation hearing that he takes seriously the department regulations that say Mueller's report should be confidential.
Current law states that the Mueller Report must be turned over to the attorney general, in this case the Trump-appointed AG, William Barr. Texas Rep. Will Hurd, a member of the House intelligence committee, said he believes the resolution should have been even broader.
Democratic Rep. Jerrold Nadler of NY, who also chairs the powerful House Judiciary Committee, introduced the resolution.
"Those are also going to be things that we are going to have to litigate", Collins said.