McCanns are furious after reports they killed Madeleine with sedatives

The missing girl's normally mild-mannered father Gerry could barely contain his anger at the smear, which accused him and his wife Kate of accidentally killing their daughter with an overdose of sedatives.

He also hit out at anonymous police sources behind the whispering campaign being waged against the couple, signalling that their relations with detectives have sunk to a new low.

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In a wide-ranging interview with British newspapers including the Daily Mail, Mr McCann also said he is considering going back to his job as a consultant cardiologist but his wife could not yet face returning to her GP work.

The couple, from Rothley, Leicestershire, do not rule out having another child but Mr McCann said they had not considered doing so and stressed that nothing could replace Madeleine.

It is 114 days since she vanished from her bed in the McCanns' holiday apartment in Praia da Luz while her parents ate tapas with friends in a nearby restaurant.

The McCanns, both 39, have remained in the Algarve with their two- year-old twins Sean and Amelie, clinging to the hope that Madeleine will be found alive.

But in the past three weeks there has been a noticeable shift in the police investigation, with detectives saying they think Madeleine is probably dead. It has led to a tide of wild speculation in the Portuguese media about her fate, and the McCanns have had to endure innuendo implying that they or their friends were somehow involved in her disappearance.

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Yesterday, Portuguese newspaper Tal & Qual went one astonishing step further. The weekly tabloid ran a front page picture of Mr and Mrs McCann alongside the headline: "Police believe parents killed Maddie".

Inside, the paper alleged Madeleine died as a result of an overdose of sedatives given to help her sleep. The McCanns, both doctors, have consistently denied giving their children any such medication.

Tal & Qual - which translates as "The way it is" - claimed Portuguese detectives "are almost absolutely certain that Madeleine was killed by accident by her parents".

The paper attributed its scoop to an anonymous source close to the investigation and even went on to speculate about the sort of prison sentences someone might get for the crimes of homicide by negligence, and hiding a body.

After learning of the story, Mr McCann was initially speechless, then said: "It's incredibly hurtful and incredibly untrue.

"Even if somebody could think that, there is just absolutely no evidence pointing in that direction.

"Without anything else, what that implies is that we somehow did it, we did it together, managed to dispose of Madeleine without a car, without anything, that the whole group was involved, that there must have been other people involved ... It is just so absurd, it is just not credible.

"But we will come through it. We will not stop and it will move on. My opinion of what has happened has not changed in 16 weeks.

"We know our facts, we know what we did. It does not bear any resemblance to this wild speculation."

Mr McCann made a blistering attack on anonymous police sources who have been feeding allegations to the Portuguese press, apparently in breach of the country's strict "secrecy of justice" laws preventing details of investigations being aired publicly.

He said: "I am disappointed that so much information is in the public domain in a country that supposedly has judicial secrecy.

"There have been whispers. There's either judicial secrecy or there's not.

"I would be perfectly happy if they said, 'Right, there is going to be nothing coming out anywhere', but that hasn't happened.

"You can't have it both ways. For Kate and I, it's an ongoing trauma and that in itself is incredibly hard.

"The wild speculation we have seen recently is detrimental. Ultimately there is an innocent four-year-old girl missing here. Some people do forget that is what this is about."

Until now, the McCanns have voiced strong support for the investigation, despite private concerns, but have been dismayed at the new direction the police investigation is taking.

The couple have several reasons for believing Madeleine was abducted, including that her favourite Cuddle Cat toy was placed by someone on a high ledge out of her reach and that one of their friends saw a man walking away from the apartment with what looked like a child in his arms.

Tal & Qual stood by its story.

The journalist who wrote it, Catarina Vaz Guerreiro, said: "I can't reveal my source but I have complete trust in them. I strongly believe the person that told us this information is telling us the truth."

But Portuguese media commentators said Tal & Qual was a "very bad sensational tabloid" not known for having good police sources.

The story was also dismissed by Portuguese police, who said it had "no authority".

Today, Mr McCann is due to be a guest speaker at the Edinburgh International Television Festival.