"Like many unsubstantiated stories in the media, this has caused unnecessary anxiety to friends and family and once again disrupted our lives.
"As we have stated many times before, we will not give a running commentary on the investigation.
"That is the job of the law enforcement agencies and we will support them in any way requested."
The couple also said that they did not have a family spokesman and are not actively paying any lawyers to represent them.
German prosecutor Hans Christian Wolters, who is leading the investigation into the main suspect in Madeleine's disappearance, told the PA news agency that a letter had been written to the couple, but he would not reveal what it said.
"I'm not able to say whether the letter has reached the family or is still on the move," he said.
"They don't know all our evidence.
"But they know that we assume that Madeleine was killed by our suspect."
Mr Wolters said prosecutors have "concrete evidence" but not "forensic evidence" that Madeleine was killed by the suspect and may "know more" than Scotland Yard, which is still treating the case as a missing person investigation.
German investigators believe 43-year-old Christian Brueckner killed Madeleine soon after abducting the toddler from a holiday apartment in the resort of Praia da Luz in May 2007.
Brueckner is in jail in Germany for drug dealing.
He is appealing against a conviction for the 2005 rape of a 72-year-old woman in Praia da Luz.
He has not yet spoken to investigators, who say they are convinced that he has committed other sex attacks.
Brueckner is a suspect in a string of unsolved crimes, reportedly including an attack on a 10-year-old British girl in Praia da Luz in 2005, one of a series of incidents in which young girls were targeted.
He is being investigated over the disappearances of Rene Hasee, who went missing at the age of six while on holiday with his family in Portugal in 1996, and Inga Gehricke, who was five when she vanished from a forest in the Saxony-Anhalt region of Germany on May 2, 2015.
It has also been reported in the German media that Brueckner is a suspect in the rape and murder of 13-year-old Tristan Brubach in Frankfurt in March 1998.