The Labour leader warned Prime Minister David Cameron that unless he stepped in to postpone the deal, he would force the issue to a potentially-damaging Commons vote.
"He has got to understand that when the public have seen the disgusting revelations that we have seen this week, the idea that this organisation, which engaged in these terrible practices, should be allowed to take over BSkyB, to get that 100% stake, without the criminal investigation having been completed and on the basis of assurances from that self-same organisation - frankly that just won't wash with the public," he told BBC1's Andrew Marr show.
News Corporation chairman Mr Murdoch is due to fly into London today to deal with the mounting fallout from the revelation of the scale of the hacking operation.
The final edition of the News of the World went on sale today after it was closed down as a result of the mounting scandal - in what Mr Murdoch said was a "collective decision".
It emerged today that police contacted Sara Payne, the mother of murdered schoolgirl Sarah Payne, to confirm she had not been phone hacked.
Child welfare campaigner Shy Keenan, who with Mrs Payne is of the Phoenix Chief Advocates group, said their names and numbers were checked against the Operation Weeting database.
Police told them yesterday that "the result of the search on the information provided is no trace within the phone billing data held by us or the evidence retrieved from Glenn Mulcaire's notes".
The BSkyB takeover bid has increasingly become the political battleground in the hacking row - with Mr Miliband hoping to exploit serious Liberal Democrat concerns to pile pressure on the Government.
While a vote on Labour's motion on Wednesday would not be binding, it would be hard for ministers not to act if MPs backed a pause.
A consultation on News Corp's bid to buy the remaining BSkyB shares it does not own ended on Friday - with the Government signalling that it could take several months before Culture Secretary Jeremy Hunt was in a position to make a ruling.
But Mr Miliband and other senior figures argue that the takeover should have been referred to the Competition Commission and have urged media regulator Ofcom to consider whether the hacking controversy alters its view on whether News Corp was "fit and proper" ti run BSkyB.
Liberal Democrat deputy leader Simon Hughes signalled his support for a delay and called on Labour to consult with the junior coalition party in a bid to formulate a motion both could support.
He told Sky News' Murnaghan: "I would suggest if Labour want our support they come and talk to us about that but if a motion can be formulated that can command wider than Labour party support, that isn't a partisan Labour motion, then I would think they would get wider support," he said.
"My recommendation to my colleagues - and it's not my final decision, it's a parliamentary party decision - would be that we as a parliamentary party make clear that it is our view that the merger should not go ahead until the criminal investigations are completed."
Energy Secretary Chris Huhne did not rule out support for a motion either but said the detail of the wording would have to be studied.
As the hacking controversy unfolded further today, Scotland Yard Assistant Commissioner John Yates expressed his "extreme regret" that he did not act to reopen police inquiries into the allegations two years ago.
Speaking after this week's revelation that the mobile phone of murdered schoolgirl Milly Dowler was among those targeted, Mr Yates, who ruled in July 2009 that there was no new evidence, told the Sunday Telegraph: "It is a matter of massive regret we didn't deal with it earlier."
Milly's family will be among hacking victims holding talks at Downing Street with Mr Cameron and Deputy Prime Minister Nick Clegg tomorrow about what action the Government is taking.
The Prime Minister announced on Friday that there would be two public inquiries, one led by a judge and looking into phone hacking by newspapers and possible corruption involving police officers taking cash for information - and another into the wider question of press regulation.
Labour has accused him of acting too slowly, blaming his links to figures such as Andy Coulson - the former News of the World editor arrested on Friday as part of the investigations into hacking and police corruption - who he employed as his Number 10 communications director.
Mr Miliband said Mr Cameron still had questions to answer about what he knew about Mr Coulson's past activities when he personally approved his appointment and said he had concerns over whether the twin inquiries would cover "all the major issues".
Talking about the takeover, he said: "After this week I don't believe it's right, and I don't believe the public will accept a position whereby this bid is waved through over the coming months, even if it is in September, on the basis of assurances from News Corporation.
"That is why we are saying the process cannot be competed by Jeremy Hunt until after this criminal investigation."
He said Ofcom "must have a chance, when this criminal investigation is complete, to consider the fit and proper person test".
"I say this to the Prime Minister candidly: I hope, over the next 72 hours, I hope he changes his position on this because I don't want to have to force this to a vote."
He said the judge-led inquiry should look beyond the News of the World and take in practices in the wider media.
Rebekah Brooks, the chief executive of News International which published the Sunday tabloid as well as the Sun, The Times and The Sunday Times, has insisted there was no reason to suspect hacking had taken place at any of the other titles.
Mr Miliband has publicly called for the resignation of Ms Brooks - who edited the News of the World at the time of the Milly Dowler hacking.
Asked if he had been warned off taking a stand, he said: "I don't think people at News International were very happy about what I have been saying this week.
"We speak to them; they were not very keen for me to say what I said."
He conceded that Labour leaders including himself had become "too close" to News International and other media groups - leading to a failure to speak out about problems.
One result of the present crisis should be to ensure politicians were no longer afraid to speak out, he said.
The News of the World signed off with the front-page headline: "Thank you & goodbye and admitted to readers in a page three apology: "Quite simply we lost our way."
Mr Miliband denied that his strategy director, Tom Baldwin, a former Times journalist, had been involved in wrongdoing.
Conservative Party donor Lord Ashcroft has alleged Mr Baldwin asked a private investigator to obtain information about his bank account.
Mr Miliband told Marr: "People are trying to make a comparison between Andy Coulson, who resigned from the News of the World over phone hacking of the Royal Family, and Tom Baldwin, who works for me.
"I think this is ridiculous, let me just explain why. Tom Baldwin was engaged in The Times newspaper including an investigation of Michael Ashcroft, about whom there was massive public interest."
Asked about the specific allegations, he said: "Tom Baldwin absolutely denies this.
"And I have to say that this is pretty desperate stuff because the Prime Minister must answer the real questions at the heart of this affair - about his error of judgment in hiring Andy Coulson and the mounting evidence there now is about the warnings that were given to him before he brought Andy Coulson into the heart of the Government machine."
Mr Miliband also renewed his demands for Mrs Brooks to be sacked.
"I think it beggars belief that Rebekah Brooks is still in her post - Rebekah Brooks was the editor at the time that Milly Dowler's phone was hacked," he said.
"The idea she's still in her post, I don't think the public can understand how that can possibly be the case."
