German prosecutors have said they believe Madeleine McCann is dead after the prime suspect in her disappearance was named.
Hans Christian Wolters, a spokesman for the Braunschweig Public Prosecutor's Office, said: "In connection with the disappearance of the 3-year-old British girl Madeleine McCann on May 3 2007 from an apartment complex in Praia da Luz, in Portugal, the Braunschweig prosecution is investigating a 43-year-old German on suspicion of murder.
"We are assuming that the girl is dead.
"With the suspect, we are talking about a sexual predator who has already been convicted of crimes against little girls and he's already serving a long sentence."
He has been named as Christian Brueckner, sources in Portugal have told Britain's Daily Telegraph.
Brueckner was initially convicted of drug trafficking and was found guilty in a German court last year of raping a pensioner in Portugal.
Clarence Mitchell - who has been a representative of the McCanns - has hinted this breakthrough is the most significant in 13 years.
He told the BBC's Radio 4 Today programme that in his time involved in the case, he cannot recall such focus on one individual, and stressed that it is the family's belief that only "two or three people maximum on the planet" know what happened to Madeleine.
On Wednesday, Scotland Yard held a press briefing, giving the most significant update in more than a decade in one of Britain's biggest unsolved mysteries.
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Wolters said the suspect was regularly living in the Algarve between 1995 and 2007, where he worked jobs in the gastronomy business, but funded his lifestyle by committing crimes, including thefts in hotel complexes and apartments, as well as drug dealing.
He added: "The Braunschweig prosecution is now concerned because before going abroad he last had his residence in Braunschweig."
German police have not ruled out a sexual motive for the alleged crime against Madeleine, which is being treated as murder by the BKA.
Christian Hoppe of the BKA added that the suspect may have broken into an apartment in the Ocean Club complex in Praia da Luz - where Madeleine was on holiday with her parents, Kate and Gerry McCann, and her twin siblings Sean and Amelie - before spontaneously kidnapping her.
A BKA appeal said: "There is reason to assume that there are other persons, apart from the suspect, who have concrete knowledge of the course of the crime and maybe also of the place where the body was left."
Mitchell said: "The German police are classing it as a murder investigation. In sharp contrast the British police are not saying that and are classing it as a missing person.
"The British police have been at pains to say there is no evidence at all she has come to harm, is dead or indeed alive.
"They are literally keeping an open mind about it."
Brueckner's identity is still hidden in Germany due to German law.
Hoppe told the country's ZDF television channel that Brueckner is serving a prison sentence for a sex crime and has two previous convictions for "sexual contact with girls".
German newspaper Braunschweiger Zeitung reported he was carrying out a seven-year prison sentence for the rape of a 72-year-old American woman in Portugal in 2005.
He is known to have been in and around the area on the Algarve coast at the time Madeleine went missing shortly before her fourth birthday.
While he is thought to have lived for some time in a camper van, police have also identified two houses he is thought to have stayed in.
Mitchell said: "The police themselves have called it a significant part of the investigation.
"It's the first time in 13 years that I can recall focusing on one individual, not named but clearly identifiable by them and the authorities, in terms of wanting to know extra detail about this movements and the vehicles he was using even down to the phone calls he was apparently receiving on the night where Maddy went missing."
He added: "In my memory of being in the case, police have never been quite so specific about an individual as they have been about this individual.
"They make the point that allegiances change. This man is in prison and if he is involved to the extent it appears, then people shouldn't be afraid to come forward now."
Brueckner has been linked to an early 1980s VW T3 Westfalia camper van - with a white upper body and yellow skirting, registered in Portugal - which was pictured in the Algarve in 2007.
Scotland Yard said he was driving the vehicle in the Praia da Luz area in the days before Madeleine's disappearance and is believed to have been living in it for days or weeks before and after May 3.
He has also been linked to a 1993 Jaguar XJR6 with a German number plate seen in Praia da Luz and surrounding areas in 2006 and 2007.
The day after Madeleine went missing, the suspect had the car re-registered in Germany under someone else's name, although it is believed the vehicle was still in Portugal.
Both vehicles - pictured below - have been seized by German police, who said there is information to suggest the suspect may have used one of them in an offence.
Reporters on Wednesday were told that Scotland Yard were taking the "really unusual" step of releasing two mobile phone numbers as part of the appeal.
The first, (+351) 912 730 680, is believed to have been used by the suspect and received a call from another Portuguese mobile, (+351) 916 510 683, while in the Praia da Luz area, starting at 7.32pm and ending at 8.02pm on the night of May 3 2007.
Madeleine is believed to have disappeared between 9.10pm and 10pm that evening.
The caller, who is not thought to have been in the Praia da Luz area, is not being treated as a suspect, but is said to be a "key witness".
Mitchell said: "The police and the private investigators brought in by the family have always thought that only two or three people maximum on the planet know what happened to Madeleine.
"In this case the police are looking at a particular phone call that I understand was received by somebody else on a Portuguese number.
"The German police and the British police have made it clear the person making the call is not a suspect but a material witness in this, which is why they've released those Portuguese numbers in the hope that they might jog somebody's memory.
"Are they in their contacts? Were they ever phoned by these numbers?
"And of course the distinctive vehicles - the camper van and the distinctive Jaguar - that he is said to have been using."
He added: "It's 13 years on, but the police still feel it's important to bring these details out now in the hope that somebody out there can still come forward and make that call."
Police are appealing for anyone who may have seen the camper van in or around Praia da Luz on the night Madeleine went missing, or in the days before or weeks after.
Detectives also want to speak with anyone who saw the van together with the Jaguar, or individually, during the spring and summer of 2007.
A statement from Madeleine's parents, read by Detective Chief Inspector Mark Cranwell, said: "We welcome the appeal today regarding the disappearance of our daughter Madeleine.
"We would like to thank the police forces involved for their continued efforts in the search for Madeleine.
"All we have ever wanted is to find her, uncover the truth and bring those responsible to justice.
"We will never give up hope of finding Madeleine alive, but whatever the outcome may be, we need to know as we need to find peace.
"We will be making no further comment in relation to the appeal today.
"We would like to thank the general public for their ongoing support and encourage anyone who has information directly related to the appeal to contact police."
Clarence Mitchell said: "Kate and Gerry do feel it's potentially very significant.
"They have welcomed the appeal, but they're not doing any interviews themselves because they wish the focus to remain on the police request rather than themselves.
"But this is an important chapter in the search for their daughter.
"They've never given up hope that she may still be alive, but they are realistic and they say whatever the outcome of this particular line of investigation, they do need to know what happened to their daughter to find peace and to bring whoever is responsible to justice."
The Cambridge graduate and rower is a career intelligence officer.