Madeleine McCann's parents are "greatly encouraged" by new information about the disappearance of their daughter, they said in a statement.
A reconstruction of the "latest, most detailed understanding" of the events around the time she went missing will be shown on BBC 'Crimewatch' on Monday, October 14.
It comes after the Metropolitan Police revealed a vast log of mobile phone traffic could be the key to finding out what happened to the then three-year-old, inset.
Scotland Yard detectives, who have interviewed 442 people as part of their review-turned-investigation into Madeleine's disappearance, hope to track down as many people present in Praia da Luz, Portugal, on or around May 3, 2007, as possible.
Madeleine's parents, Kate and Gerry McCann, said: "We are greatly encouraged by new information coming to light, with pieces of the jigsaw now fitting together. We are really hopeful that the forthcoming appeal on 'Crimewatch' will bring further new evidence, which will take us a step closer to finding Madeleine and to bringing those responsible for her abduction to justice."
Detective Chief Inspector Andy Redwood, the senior investigating officer, said: "We now believe we have the most complete picture to date of the events surrounding her disappearance.
"I truly believe there are people out there who hold the key to Madeleine's disappearance, and that so far they may be completely unaware of that fact."
'Crimewatch' editor Joe Mather said: "We've been working very closely with the Metropolitan Police on a new Madeleine McCann appeal for several months.
Last week, Scotland Yard revealed that since launching its own investigation, 41 people of interest had been identified, including 15 UK nationals, up from 38 people of interest including 12 UK nationals established in July.