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Scotland Yard want Portugese Police to re-open the search for the missing Leicestershire girl.
The Metropolitan Police issued a statement about its conclusion after conducting an investigative review into her disappearance.
Police said: "As a result of evidence uncovered during the review they now believe there is a possibility Madeleine is still alive and are appealing for anyone who is able to provide direct information as to her whereabouts to contact the team."
Madeleine disappeared on May 3, 2007 during a family holiday at a resort in Portugal's Praia da Luz. A huge hunt was launched after she went missing while her parents Kate and Gerry dined with friends nearby but she has never been found.
Her parents, both doctors who live in Rothley, Leicestershire, have battled to retain the case's high-profile.
The police investigative review was commenced in May 2011 under the leadership of the then commissioner, Sir Paul Stephenson.
A murder team within the Homicide and Serious Crime Command conducted the review and the team worked in close collaboration with a senior investigating officer from Portugal's Policia Judaria.
"Throughout the course of the review officers have been in close contact with the McCann family who have been assigned a family liaison officer as is standard in accordance with national family liaison policy," Scotland Yard said.
"Officers are now methodically going through that material which they believe amounts to around 40,000 pieces of information equating to approximately 100,000 pages."
British detectives travelled to Portugal several times as part of the investigation.
"The intention is to identify from that material investigative opportunities which we will then present to the Portuguese authorities who retain primacy for the investigation," police said.
"Officers have so far identified around 195 such opportunities within the historic material, and are also developing what they believe to be genuinely new material."
Meanwhile, the police commissioned the computer-generated likeness of Madeleine as a nine-year-old, as the fifth anniversary of her disappearance approaches.
The picture was created by Teri Blythe, who is a specialist in forensic art services for both missing persons and unidentified cases.
Police added: "The second point of appeal today is in relation to those who were at the resort of Praia da Luz between 28 April and 3 May 2007.
If you were either on holiday or in residence in the resort during this period, particularly in the vicinity of the Ocean Club, and you have not been spoken to by police either here or in Portugal then please call us on 0800 096 1011 if you are within the UK." ::
The number for non-UK residents is +44 20 7158 0126. Alternatively, Crimestoppers can be contacted anonymously in Britain on 0800 555 111.
(c) Sky News 2012