Madeleine McCann's parents are "greatly encouraged" by new information about the disappearance of their daughter, they said in a statement.
Madeleine went missing from a holiday apartment in Portugal in 2007.
It was nine days before her fourth birthday, as her parents dined at a nearby tapas restaurant with friends.
A reconstruction of the "latest, most detailed understanding" of the events around the time she went missing will be shown on the BBC Crimewatch programme on Monday, 14 October.
It comes after London's Metropolitan Police revealed a vast log of mobile phone traffic could be the key to finding out what happened to Madeline, who disappeared aged three in 2007.
Scotland Yard detectives have interviewed 442 people as part of their review-turned-investigation into Madeleine's disappearance.
They hope to track down as many people present in Praia da Luz, Portugal, on or around 3 May 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."
A three-year-old actress is to play Madeleine in the Crimewatch reconstruction, as a small production team from the programme spent a week filming abroad for the new appeal.
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.
"We are now making targeted and new appeals for help from the public. 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 presenter Kirsty Young speaks to the McCanns in the new programme, while presenter Matthew Amroliwala has been to Praia da Luz to explore the new focus of the police investigation.
Earlier this week, Scotland Yard revealed that since launching its own investigation, 41 people of interest have been identified.
Included are 15 UK nationals, up from 38 people of interest including 12 UK nationals established in July.
Detectives have issued 31 international letters of request to mostly European countries.
The letters are in relation to some of the persons of interest as well as accessing phone records.
A large but "manageable" list of phone numbers identified as being present in Praia da Luz - though not necessarily used to make phone calls - has been drawn up by detectives with a "significant" number unattributed to any named person.
Significantly, police officers are now able to create a log showing calls being made at the time of Madeleine's disappearance.
The latest appeal will also be broadcast in Holland and Germany.