Kate and Gerry McCann believe a bag of discarded clothes said to have a DNA link to Madeleine proves she is still alive.
The plastic bag, found dumped near Faro airport in Portugal two weeks ago.
The discarded white carrier, which was discovered 75miles from where the four-year-old vanished, contained a shower curtain, a white flannel, a green elastic band, a green child's T-shirt with a flower on the front and a pencil case with a pink heart motif.
Crucially, there was also a pair of adult's jeans and a fleece which had traces of body fluid and hair with a partial DNA match to Madeleine.
A friend of the McCanns said: "Kate and Gerry are very encouraged by news of this development, which on the face of it seems to be extremely significant.
"Obviously if there are items linked by DNA to Madeleine then that raises important questions about how they got there and who put them there.
"However, the fact that they were found so recently does suggest that Madeleine could still be alive and that her abductor is active close to Praia da Luz.
"This is obviously incredibly encouraging for Kate and Gerry and backs up what they have always said, which is that Madeleine was taken."
The carrier bag, which was discovered by a member of the public, is the first significant clue found outside the McCanns' Praia da Luz holiday apartment in the six months since Madeleine vanished on May 3.
The bag and its contents were sent to the Forensic Science Service lab in Birmingham for DNA analysis.
It is believed the fleece and the jeans, which had more than 60 different stains on them, contained a "moderate" DNA match to Madeleine. It was rated three on a scale of eight.
A source said: "The bag could be crucial. The DNA isn't an exact match to MADDY'S but it does link. The blue fleece and jeans were found to contain traces of congealed skin and hair.
"They were found to contain DNA characteristics that could be attributed to Madeleine McCann. It is the first clue found outside the apartment complex and could provide a trail."
Police are waiting for further test results to see if any other DNA is discovered. If so, it will be checked against a list of known sex offenders.
Forensic expert Dr John Manlove said yesterday: "If a crime stain produces a DNA profile that is not an exact match with a reference sample from a known individual then the DNA in the crime stain could not have originated from that individual. However, if there are many parts of similarity between the two DNA profiles, it should be considered that the individuals may be related."
Madeleine did not own a pencil case or a similar T-shirt. The McCanns believe that if the bag is linked to their daughter, then those items may have been bought by her abductor.
And a friend said none of the adult clothes found matched any items belonging to either Kate or Gerry.
He added: "Kate and Gerry do not own a blue fleece, and never did during their time in Portugal. They are puzzled by the green T-shirt and pencil case which have reportedly been found because Madeleine was wearing pyjamas when she disappeared and did not have a pencil case like the one described."
Meanwhile it was reported yesterday that four of the seven friends the McCanns dined with on the night of May 3 could also be made official suspects in the case.