BBC director of news Helen Boaden and her deputy Steve Mitchell have been asked to "step aside" pending the outcome of an internal review into the handling of the Jimmy Savile claims.
It follows a report into a separate Newsnight broadcast on abuse claims, which said the BBC must resolve a "lack of clarity" in the chain of command.
The director general quit over the broadcast with a £450,000 pay-off.
Downing Street said it was "hard to justify" such a sum.
Sources told the BBC that Prime Minister David Cameron believes it was a matter for George Entwistle's conscience as to whether he expected the full payoff - a year's salary after just two months in the job.
Culture secretary Maria Miller said: "The [BBC] Trust will need to justify this - it is accountable to licence fee payers in ensuring value for money, and we expect it to have considered that carefully."
Labour has asked for an urgent question in the House of Commons on the pay-out.
Mr Entwistle resigned following a Newsnight report which led to former Tory treasurer, Lord McAlpine, being wrongly accused of child abuse in north Wales in the 1980s.
The BBC said neither Ms Boaden nor Mr Mitchell "had anything at all to do with the failed Newnight investigation into Lord McAlpine".
However, they were in the chain of command at the time that Newsnight shelved an earlier investigation into abuse claims against former BBC presenter Jimmy Savile.
They had removed themselves from making decisions on some areas of BBC News output while a separate inquiry, by former head of Sky News Nick Pollard, was held into that decision.
Ken MacQuarrie, director of BBC Scotland, in his report on the north Wales broadcast, said: "To address the lack of clarity around the editorial chain of command, a decision has been taken to re-establish a single management to deal with all output, Savile-related or otherwise.
"Helen Boaden has decided that she is not in a position to undertake this responsibility until the Pollard review has concluded."
He added: "Consideration is now being given to the extent to which individuals should be asked to account further for their actions and if appropriate, disciplinary action will be taken."
The BBC said once the Pollard Review reports, Ms Boaden and Mr Mitchell "expect to then return to their positions".
The director of news has overall editorial and managerial responsibility for UK-wide and global news and current affairs on radio, television and online.
Fran Unsworth, head of newsgathering, and Ceri Thomas, editor of BBC's Radio 4 Today programme have been asked to fill the respective roles, for the time being.
The acting director general of the BBC, Tim Davie, told staff by email on Monday that there would be "no handbrake turn" in implementing work started by Mr Entwistle on "getting rid of anything that gets in the way of delivering the best of British creativity to our audiences".
BBC business editor Robert Peston said he had learned that lawyers acting for Ms Boaden and Mr Mitchell have informed Mr Davie that they are quite capable of running BBC News, even with the uncertainty created by the Pollard inquiry.
BBC Trust chairman Lord Patten, who appointed Mr Entwistle, has faced calls from MPs to resign over the affair, but Mr Cameron said "the important thing is for Chris Patten to lead the BBC out of its present difficulties".
Regarding Mr Entwistle's pay-out, Labour's deputy leader Harriet Harman has called for an urgent question in the House of Commons on the issue, saying "it looks like a reward for failure".
She has called on him not to take more than the six months' pay-off he is contractually entitled to.
When details were released, a BBC Trust spokesman said the figure was in lieu of notice.
"This reflects the fact that he will continue to help on BBC business, most specifically the two ongoing inquiries," he said.
Also on Monday a journalist involved with the north Wales investigation quit his job at the Bureau of Investigative Journalism. BIJ editor Iain Overton had tweeted before broadcast that Newsnight was going to link a senior political figure with paedophilia.
Chain of command
Meanwhile, more details have emerged about the decision-making process behind Newsnight's north Wales care home abuse story.
The controller of Radio 5 live, Adrian Van Klaveren, was in overall charge of the investigation, and he reported to a member of the BBC's management board, the BBC Northern Ireland director Peter Johnston.
BBC broadcaster David Dimbleby said Mr Entwistle was not suited to the job.
"The fact he chose to resign rather than fight showed he wasn't actually the right choice for director general, admirable man though he may be.
"If you're going to be the DG you've got to fight for the organisation, and you've got to fight for the many people who work for it."
Apart from BBC inquiries into the Savile and north Wales abuse claims, there are numerous separate investigations ongoing, including by police into historic and fresh claims, the NHS, and the director of public prosecutions, and independent figures reviewing previous investigations.