Speaking for the first time about the police operation, they urged people to 'refrain from spreading rumours' as detectives began searching the underground sewerage network in Praia da Luz.
According to the Mirror, police are carrying out DNA tests on scraps of clothing they found in a hidden pit just feet from where Madeleine vanished.
Forensic experts drafted in from the UK are carrying out analysis of the 'non-organic' material, which was found near a hole in the ground on wasteland in the resort.
Kate and Gerry urged caution, saying on Facebook: "We would like to ask people to refrain from spreading rumours and speculation based on inaccurate press reporting.
"We are kept updated on the ongoing work in Portugal and are encouraged by the progress.
"Thank you for continuing to stand by us and supporting our efforts to get Madeleine home."
Madeleine McCann went missing in May 2007, aged three. An administrator for the Official Find Madeleine Facebook page said her parents, from Rothley in Leicestershire, had been asked not to visit Praia da Luz while the search is under way.
A post on the page said: "To those commenting on why Gerry and Kate are not in Portugal, it's because they were asked to not go there. Please let the police do their job.
"And anyone posting their sanctimonious comments about leaving children alone will be banned. No questions asked. We've heard it all before. ENOUGH with the judging."
The McCanns' statement came at the end of the a fifth day of searches in a 15-acre spread of dense scrubland, where officers on Thursday prised open manholes and inspected sewer pipes using micro cameras and fibre optic cables.