Democrat Jerry Nadler accused William Barr of failing to let “the facts speak for themselves” over his plans to hold a news conference before the release.
The 400-page report is the result of an investigation into alleged Russian interference during the 2016 election.
A summary, released by Mr Barr, reveals it clears Mr Trump of any collusion.
However, it does not go as far as to completely exonerate the president of obstruction of justice.
Both Mr Trump’s supporters and detractors are now eagerly awaiting the full – albeit redacted – report’s release.
It will be sent to Congress between 11:00 and midday local time (15:00 GMT and 16:00 GMT). It will be published online sometime after this.
Mr Barr is due to hold a news conference at 09:30.
What is the Mueller report?
The report contains the findings of a 22-month investigation into possible collusion between Russia and the Trump presidential campaign back in 2016.
It was led by Special Counsel Robert Mueller, who was chosen to run the investigation in 2017 following concerns from US intelligence agencies that Russia had tried to tip the election in Mr Trump’s favour.
He also looked into whether Mr Trump obstructed justice when he asked for the inquiry into former national security adviser Michael Flynn to end, and later fired FBI chief James Comey.
Mr Flynn has since pleaded guilty to lying to the FBI about his contacts with Russia – one of six former Trump aides and 30 other people, including 12 Russians, charged in connection with the investigation.
What do we know already?
So far all the public have seen of the report is the four-page summary released by US Attorney General Barr.
It contained Mr Mueller’s main conclusions. The first, that Mr Trump did not collude with Russia during the 2016 campaign, and the second, that he did not completely exonerate him of the charge of obstructing justice.
He said: “While this report does not conclude that the President committed a crime, it also does not exonerate him.”
Exactly what this means is what many hope to discover with the release of the report on Thursday.
But it may not be that easy to ascertain. The report has been redacted, with a colour-code indicating the reasons why.
As a result, according to the BBC’s North America editor Jon Sopel, “it might look more like a colouring book than a report”.
How has President Trump reacted?
Mr Trump and his supporters immediately jumped on the fact that no collusion was found.
“After three years of lies and smears and slander, the Russia hoax is finally dead. The collusion delusion is over,” the president told a cheering crowd in Grand Rapids, Michigan, last month.
The Republican president has repeatedly described the investigation as “a witch hunt”.
However, he has not addressed the fact that the report does not completely clear him of the allegation of obstructing justice.
What do his opponents say?
Leading Democrats have called for the Mueller report to be published in full, and pledged to make use of the party’s majority control of committees in the House of Representatives to continue investigating the president.
They have also raised concerns over Mr Barr’s handling of the report since Mr Mueller’s team handed it to the Justice Department.
A joint statement, signed by the Democratic chairs of five House committees, said the press conference was “unnecessary and inappropriate, and appears designed to shape public perceptions of the report before anyone can read it”.
“Rather than letting the facts of the report speak for themselves, the Attorney General has taken unprecedented steps to spin Mueller’s nearly two-year investigation,” Mr Nadler, who is the House Judiciary Committee chairman, added while speaking to reporters on Wednesday.