Kate and Gerry McCann said in a statement on the Find Madeleine website that reports about the correspondence were "unsubstantiated" and had caused "unnecessary anxiety" to their friends and family.
In the post, they said: "The widely reported news that we have received a letter from the German authorities that states there is evidence or proof that Madeleine is dead is false,"
"Like many unsubstantiated stories in the media, this has caused unnecessary anxiety to friends and family and once again disrupted our lives," they added.
The couple also stressed that they would not give a "running commentary" on the case, before saying that any developments in the investigation would come from law enforcement agencies.
The statement from the McCanns comes after German prosecutor Hans Christian Wolters told the Press Association that a letter had been written to them, without specifying the content of the correspondence.
However, the Sun quoted Mr Wolters as saying: "We have written to the McCanns to tell them Madeleine is dead and explaining we just cannot say what the evidence is."
According to the paper, the prosecutor added that the German authorities have shared an overview of their findings with Scotland Yard.
Investigators in Germany think that Christian Brueckner, 43, abducted Madeleine from a holiday apartment in Praia da Luz, Portugal, in 2007, before killing her.
Brueckner is currently serving a sentence in Germany for drug dealing and for raping a 72-year-old woman in Portugal in 2005.
The German authorities believe he may be linked to several other unsolved crimes, including the disappearances of a 6-year-old boy in Portugal in 1996 and a 5-year-old from a forest in Germany in 2015.
German media have also reported that Brueckner is a suspect in the rape and murder of 13-year-old Tristan Brubach in Frankfurt in March 1998
Additional reporting from the Press Association