Madeleine McCann was killed in her familys holiday apartment when she screamed out in alarm at a paedophile intruder, it has been claimed.
Police believe the three-year-old may have been accidentally suffocated by a prowler who panicked when she shouted out.
Fearing that her cries would raise the alarm, he violently silenced her - accidentally killing her - and then grabbed her body and escaped, according to the new theory.
It was that fleeing man - carrying the slumped body of a child - who was spotted by the McCanns' friend Jane Tanner, it was claimed.
The theory was revealed in the respected Portuguese newspaper Publico, which carried a chilling recreation of the supposed chain of events.
The newspaper said the theory was "gaining increasing strength at the centre of the police investigation". It came a week after Portugal's Attorney General Fernando Pinto Monteiro said he believed Madeleine was "probably dead".
The latest theory came as a blow to Kate and Gerry McCann, who have insisted they believe their daughter is being held somewhere alive.
But it does suggest that detectives are moving away from the belief that the couple were involved in her disappearance.
They are now working on the theory that a prowler monitored the family's routine during their week-long holiday, and carefully chose a moment to strike, Publico reported.
The couple's regular habits - including their meal times and their routine in checking on their children - made it 'easy' for the intruder to pick a moment when he did not think he would be disturbed, the newspaper claimed.
It carried a highly dramatised recreation of the supposed chain of events, which said: "An unexpected event thwarted the prospect of desire. A shout from the British child awakened from her sleep.
"The fear that she would be heard, the urgency to silence her, the violence, probably the suffocation and the unexpected death. "All this is in minutes. Now one would have to take her out of there, close the door, escape quickly."
The theory was said to be "seriously considered" by senior police officers leading the investigation, but they have not ruled out other possibilities, including that the McCanns could have been involved.
Their spokesman Clarence Mitchell said the report was "extremely distressing" for the couple.
He said: "We do not believe that this is what happened to Madeleine. There has been no evidence to suggest this happened in the apartment at all.
"We are still firmly of the belief that Madeleine is alive and will be found."
The couple were named as official suspects in the case after specialist sniffer dogs detected microscopic traces of blood in their holiday apartment, and the "scent of death" in their hire car.
They have always insisted they believe Madeleine was taken alive from the apartment, and that their friend Miss Tanner saw the suspect fleeing with her.
A source close to the couple said the theory that a paedophile killed her inside the flat and then carried her body away was "ludicrous".
He said: "It is an absolutely ludicrous suggestion. If a paedophile had killed her in the apartment he would have left her there and fled.
"There is no way he would have carried her dead body through the streets where people would have witnessed it."
Mr McCann has told police he checked on the children at about 9pm, and then bumped into a friend, television producer Jeremy Wilkins, and stopped to speak to him.
While the two men were speaking the McCanns' friend Miss Tanner - one of the so-called Tapas Nine - said she walked past them and then saw the fleeing man moments later, at about 9.15pm.
Mr McCann has spoken of his belief that an intruder might have been hiding inside the flat already when he went to check on the children.
But it would still only give the alleged paedophile just a few minutes to supposedly disturb Madeleine into screaming, to accidentally suffocate her and then flee with her body by 9.15pm.
McCann spokesman Mr Mitchell said he did not believe an intruder would have had time to kill Madeleine and escape.
He said: "Any abductor would not have had time to do what is alleged here.
"The only point in this report to draw comfort from is the indication that police no longer believe that Kate and Gerry are involved in Madeleine's disappearance."
A nanny who used to work at the Ocean Club holiday complex has told the McCanns' private detectives that she saw a man trying to lift the window shutters at the same apartment where the McCanns later stayed.
The woman, who has not been named, said the man she saw in December last year looked like the other official suspect in the case, British expat Robert Murat.
His friends dismissed the alleged sighting as a smear and said it could not have been the 34-year-old as he was in Britain from October to January this year.
Miss Tanner has told the McCanns that she could not tell if the man she saw was Mr Murat, as she did not see his face. He denies any involvement in Madeleine's disappearance.
An investigating judge has to decide early next year whether to end the secrecy surrounding the Madeleine McCann case - and decide whether to let her parents and Robert Murat see the police evidence against them.
Heart surgeon Gerry and GP Kate, both 39, have always protested their innocence and claimed an intruder took their daughter.
The McCanns have rubbished the suggestion - thought to have been top of the police list of theories until now - that Madeleine died by accident in their apartment and they disposed of her body as part of a "cover-up."
Claims emerged last night that Portuguese police had initially considered whether the couple could have sold their daughter to paedophiles.
Detectives reportedly believed the couple might have sold Madeleine to a criminal network to ease money worries.
According to sources, they spent "several days" investigating but the wild theory fell apart when they realised the couple were wealthy.
A police source told the Portuguese newspaper 24 Horas: "The police team in charge of the case investigated the possibility that the child had been sold by her own parents because of financial difficulties."
Detectives tried to inspect bank statements but were forced to conclude that the couple did not have money problems.
The McCanns, who are both doctors, live in a �500,000 house in Rothley, Leicestershire. Police were said to be suspicious about reports that Mrs McCann screamed: "They've taken her" when she realised Madeleine was missing. She insists she shouted: "She's gone."
Detectives have been unable to seize the couple's bank statements, phone records covering this May or their medical records.
The public prosecutor in the case has refused to authorise such moves unless he sees stronger evidence against them.