Kate and Gerry McCann were left furious after a disgraced detective claimed the couple could have hidden their daughter Madeleine's body inside the coffin of a woman.
Portuguese officer Goncalo Amaral made the outrageous allegations as his libel trial was delayed for the fourth time after he sacked his lawyer.
Speaking earlier to a Portuguese newspaper and its TV channel, Amaral, who was sacked after botching the initial hunt for Madeleine, repeated his claims that she is dead.
But he suggested the McCanns hid Madeleine's body in the woman's coffin at Praia da Luz catholic church – which they had a key for – a month after she vanished in 2007.
Amaral added: "The mystery will only end when the McCann couple are no longer being protected. Only then will we understand the truth."
But a source close to the couple told the Mirror: "These are sickening allegations that no sane person would believe.
"It's about time people realised what Mr Amaral is, a liar and a fantasist. He has been making these false claims since he was sacked.
"He is suggesting Kate and Gerry moved Madeleine's body a month after she vanished. At that time they were the most-watched couple in the history of the modern media."
Kate, 46, and Gerry, 45, arrived at the Palace of Justice yesterday for the long-awaited libel hearing.
But the judge adjourned the case after Amaral revealed he had fired his lawyer.
Kate said outside court: "Every time he postpones the case it brings us more pain and distress. We just want justice. This is not fair."
Gerry added: "We're exasperated that the hearing has been cancelled once again at Mr Amaral's request. This is the fourth time.
"We want to get justice for Madeleine. Today is a blatant and cynical attempt to wear us down and it's Madeleine who is suffering. We're not giving up."
Amaral's libel case began in 2009 over his book The Truth of the Lie. In it he claims Madeleine died inside the couple's holiday flat and they covered it up. The couple deny the allegations.
The hearing was adjourned until July 8.