Madeleine McCann's parents have said the identification of a new prime suspect in her disappearance is "the most significant development in 13 years."
Police said a 43-year-old German who is in jail in his homeland for child sexual offences was now suspected of involvement in the little girl's disappearance.
The man, whom they did not name, was in Praia da Luz on the day of Madeleine's disappearance and received a telephone call in the area an hour before the girl vanished.
Officers said he had lived in Portugal between 1995 and 2007 and released images of two vehicles belonging to the man who is now their main suspect.
A representative for Madeleine's parents, Kate and Gerry McCann, said this morning that the development is "very significant."
Spokesman Clarence Mitchell told Sky News today: "From everything police are saying and doing, this would appear to be the most significant lead that they are trying to close down in the 13 years since Madeleine disappeared."
Mr Mitchell also told BBC radio: "They've never given up hope that she may still be found alive but they are realistic.
"Whatever the outcome of this particular line of investigation maybe, they do need to know what happened to their daughter to find peace and to bring whoever is responsible to justice."
Senior police officers described the line of inquiry as "significant" as they appealed for information over the whereabouts of the German at the time Madeleine went missing aged just three in May 2007. Friends of Kate and Gerry McCann said it was the biggest development in the case since their daughter went missing and the first time that two separate forces - in Britain and in Germany - had publicly identified a suspect.
In an earlier statement yetserday, the girl's parents, both doctors, said: "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."
They said they welcomed a renewed call made jointly by British, German and Portuguese police to find Madeleine and trace the movements of the suspect.
In a coordinated appeal for information, broadcast on German television, authorities there said the man was suspected of Madeleine's murder.
He was described as a "multiple" child sex offender serving a lengthy jail term. During his time in the Algarve, he did odd jobs but is also thought to be implicated in hotel and holiday home burglaries and drug dealing.
The suspect first came to the attention of the Metropolitan Police's Operation Grange unit after an appeal was made marking the 10th anniversary of Madeleine's disappearance in 2017. The Met asked for help from their German counterparts, the Bundeskriminalamt, six months later in November 2017. It is unclear why it has taken almost three years for officers to go public.
In a statement, Scotland Yard said: "Met detectives working with German authorities have identified a man currently imprisoned in Germany as a suspect in Madeleine's disappearance."
Police insisted the case remained a "missing persons" inquiry but the public identification of the suspect suggests they believe she was abducted.
Detectives tracing the suspect's mobile phone calls at the time have established the German national was in Praia da Luz an hour before Madeleine went missing. He received a call on his mobile phone that lasted half an hour from 7.32pm to 8.02pm. Madeleine went missing at some time after 9pm.
The suspect, who was 30 at the time, was then living in a distinctive VW T3 Westfalia camper van with a white upper body and yellow skirting. Police described the man as an "itinerant" who had lived on and off in the area from 1995 until 2007.
Officers refused to be drawn on whether the van with a Portuguese number plate might have been used in Madeleine's abduction.
Police forces are also seeking information on a second car, owned by the suspect, which he kept in the Algarve. The car, a 1993 Jaguar saloon with German number plates, was registered in his name, but the registration changed to somebody else on May 4 2007, the day after Madeleine vanished.
Police said: "To re-register the car in Germany you don't have to have the car in the country or region. We believe the car was still in Portugal and would like information if you saw it."
The Metropolitan Police also took the highly unusual step last night of releasing the Portuguese mobile phone number the suspect was using at the time and the number of the person who called him. Police are trying to discover who called the man.
"Investigators believe the person who made this call is a highly significant witness and are appealing for them to get in touch," said the Met.
Scotland Yard also published photographs of both the VW camper van and the Jaguar XJR 6, both now in possession of German police.
It is understood that police in the UK and Germany have interviewed the suspect in jail but that he has declined to help with their inquiries.
It is also understood forensic testing has been carried out on both vehicles.
Scotland Yard said the man was "white and in 2007 is believed to have had short blond hair, possibly fair.
@He was about 6ft... with a slim build. He is 43 years old, but in 2007 may have looked between 25 to early 30s.
"He is connected to the area of Praia da Luz and spent some short spells in Germany. This individual, who we will not identify, is currently in prison in Germany for an unrelated matter."
It is understood British officers stopped short of naming him to avoid breaching German privacy laws.
Christian Hoppe, of Germany's Federal Criminal Police Office, told the media the suspect has two previous convictions for "sexual contact with girls."
He said that police were not ruling out a sexual motive and that the suspect may have broken into the apartment and spontaneously committed the kidnapping.
One of the first things people instinctively do when a toddler goes missing in a holiday resort is check all the nearby swimming pools. Every year, several hundred kids around the world accidentally drown in swimming pools when they wander off from their parents.