The BBC is to review its editorial practices and investigate how journalist Martin Bashir was rehired, following an inquiry into his interview with Diana, Princess of Wales.
Lord Dyson's report found the BBC covered up "deceitful behaviour" used by Bashir to secure the interview.
The BBC board accepted the findings in full and reiterated its apology.
Culture minister John Whittingdale told MPs that the BBC had "damaged its reputation" in the UK and abroad.
The inquiry, published last week, found Bashir had faked bank statements designed to suggest Princess Diana was under surveillance - to win the trust of her brother Earl Spencer, and eventually gain access to the princess for the 1995 Panorama interview.
As media interest in the interview increased, the BBC covered up what it had learned about how Bashir secured the interview, the inquiry said.
The Duke of Cambridge said his mother was failed "not just by a rogue reporter" but by BBC bosses.
The BBC rehired Bashir as religion correspondent in 2016, when questions had already been asked about his conduct.
It said the post was filled after a competitive interview process.
But Mr Knight, chairman of the Digital, Culture, Media and Sport Select Committee, told the House of Commons on Monday the BBC rehired and promoted Bashir "who they know was a liar."
He said: "My sources suggest Mr Bashir wasn't interviewed, he was simply appointed. Hardly a highly competitive process."
However, the BBC said Mr Knight was not correct on that point, adding: "We can confirm there was an interview process for this position, and that Martin Bashir was interviewed as part of that."
Mr Knight also said the Dyson report left more unanswered questions such as "who was precisely involved in the 25-year cover-up and instituted the action against whistleblowers?"
He also asked: "Was Bashir rehired in essence so that he would keep his mouth shut?"
Bashir, who was promoted to religion editor after his rehiring, has since resigned without a pay-off.
The BBC board said in a statement it hoped to ensure the "mistakes of the past" could not be repeated.
"We accepted Lord Dyson's findings in full and reiterate the apology we have offered to all those affected by the failings identified," it said.
"We recognise the impact that the events it describes has had on so many people, not least those whose lives were personally affected by what happened. We also acknowledge that audiences had a right to expect better from the BBC."
The board said it had "confidence" that the "processes and guidelines in today's BBC are much stronger than they were in 1995".
But it said "it is right that we review the effectiveness of the BBC's editorial policies and governance in detail".
Dame Melanie Dawes, Ofcom's chief executive, said: "We've told the BBC that we expect its review to draw from a range of broadcasting expertise. We have also highlighted the need for greater openness and transparency at the BBC in order to maintain public trust, and will pay close attention to the review as it proceeds."
BBC chairman Richard Sharp told the BBC's World at One: "I take comfort from the fact that Martin Bashir is no longer here. I don't take comfort yet from understanding why he was rehired. We will find that out."
Asked what he knew of Bashir's rehiring, including whether due diligence was carried out, he said: "I actually don't know, that is being examined by the executive and they will report to the board on that. "I want to see the facts."
Mr Sharp said that there was "no doubt... that the practices adopted in advance of the interview were entirely unacceptable in any ethical news journalism broadcasting entity, and that was a clear failure".
He added: "It's also clear that the approach to reviewing the programme and the practices failed. And that's a separate failure which was identified in the prince's statement to do with governance, accountability and scrutiny."
Mr Whittingdale told the Commons on Monday the government should not interfere in editorial decisions, but ensure there was "a strong and robust system of governance at the BBC with effective external oversight."
He said: "The BBC has been and should be a beacon, setting standards to which others can aspire. That it has fallen short so badly has damaged its reputation both here and across the world."
Mr Whittingdale said there was "no question of dismantling the BBC or defunding it".
The BBC now needs urgently to demonstrate that these failings have been addressed and that this can never happen again, he said.
The Panorama interview featured Princess Diana giving an extraordinarily frank account of her marriage to the Prince of Wales, famously saying "there were three of us in this marriage" - a reference to her husband's affair with the future Duchess of Cornwall and admitting to an affair of her own.
Richard Sharp's intervention is significant partly because it is the first time a BBC figure has spoken since Prince William's statement.
He made clear that his concern was not only the (lack of) integrity of the original broadcast, but the "culture" that allowed Bashir's deceit and the subsequent "woeful" investigation.
The focus of this story is moving on, as Sharp acknowledged, to why Bashir was rehired by the BBC in 2016.
He was an employee of the BBC until this month.
As the clamour for reforms grow, this re-entry of Bashir to the BBC, and his subsequent promotion, undermines any hopes the corporation had that it could argue this all belongs to the past.
James Harding, who was director of BBC News when Bashir was rehired, said last week that he had not known the journalist had forged bank statements and, had he known, "he wouldn't have got the job".
Asked about whether he had consulted then-director general Lord Hall about the reappointment, Mr Harding, who left the BBC at the beginning of 2018, did not answer directly but said he himself took responsibility for Bashir's rehiring.
Lord Dyson's report, published last Thursday, said the BBC had fallen short of "high standards of integrity and transparency" over the interview.
The report said an internal BBC investigation in 1996, led by Lord Hall, into the initial complaints had been "woefully ineffective".
The independent inquiry was commissioned by the BBC last year, after Diana's brother, Earl Spencer, questioned Bashir's tactics to get the interview.
Lord Dyson found that Bashir had lied to BBC managers about deceiving Earl Spencer with the forged bank statements.
The inquiry said Bashir told his bosses he had not shown the fake documents to anyone.
The report described significant parts of Bashir's account of the events of 1995 as "incredible, unreliable, and in some cases dishonest".
Bashir has said mocking up the documents "was a stupid thing to do" and that he regretted it, but said they had had no bearing on Diana's decision to be interviewed.
Speaking to the Sunday Times, Bashir said he was "deeply sorry" to her sons, the dukes of Cambridge and Sussex.
But he rejected Prince William's claim that he had fuelled her paranoia, saying they were close and he "loved" her.
Following the report's publication, the Duke of Cambridge said the deception fuelled his mother's paranoia and worsened his parents' relationship.
Due to the way it was obtained, Prince William has said the interview should not be shown again.