Mueller was supposed to testify before the House Judiciary and Intelligence Committees on July 17 in two consecutive hearings, each scheduled to last about two hours.
Lawmakers from both parties have said they are eager to question the former special counsel about both his conclusions and the handling of the Russian Federation investigation, which Trump has repeatedly called a "witch hunt".
Under the new arrangement, Mr Mueller will testify for an extended period of time - three hours instead of two - before the House Judiciary Committee. "After a brief break, the House Intelligence Committee will convene for additional public testimony beginning at 12:00 p.m".
His appearance was thrown into disarray when lawmakers complained about the time allotted for committee members to ask questions.
Mueller said because of longstanding Justice Department regulations that a sitting president can not be indicted, his team of investigators didn't consider trying to indict Trump.
However, lawmakers are banking on public testimony to reveal the contents of the report to Americans who have not read it.
They want to extract information from the former special counsel and spotlight what they say are his most damaging findings against US President Donald Trump.
Mueller's investigation didn't discover proof of collusion between Russian Federation and the Trump 2016 presidential marketing campaign.
Saying that Mr. Mueller has already made determined his conclusions, the president added, "You might perchance perchance perhaps well presumably most effective win so many bites at the apple". But Democrats want to know more about how he made that decision and when.
He will now appear first before the House Judiciary Committee on the set date and later for another two hours before the Intelligence Committee. Both House panels had expected to have a chance to question the deputies, Aaron Zebley and James L. Quarles III, in private after Mr. Mueller's public testimony.
Mueller had been scheduled to appear on July 17 before the House Judiciary and Intelligence committees in back-to-back sessions where 22 members from each committee would get to question the special counsel. Debbie Lesko, a junior GOP member of the panel. It isn't clear when new hearings might take place.
It's unclear whether Mueller's testimony will give Democratic investigations new momentum. The people requested anonymity because they weren't authorized to speak publicly.
Trump and Barr had opposed to Mueller testifying before the Congress.
Republican protests concerning the preparations boiled over earlier this week, when Republicans accused Schiff of upstaging the Judiciary Committee, regardless of its main jurisdiction over particular counsel investigations.