Investigations have so far failed to find Madeleine McCann
The parents of Madeleine McCann are to sue former Portuguese police detective Goncalo Amaral for defamation.
Kate and Gerry McCann are taking action over "unfounded and grossly defamatory claims", their spokesman said.
Mr Amaral, who led the inquiry into the Madeleine's disappearance but was taken off the case in October 2007, told Portuguese TV he would counter sue.
Madeleine, of Rothley, Leicestershire, was three when she vanished from the Algarve holiday flat on 3 May 2007.
In a statement, the parents of the missing girl said: "We - together with our three children Madeleine, Sean and Amelie - are taking this legal action against Goncalo Amaral over his entirely unfounded and grossly defamatory claims.
"[They were] made in all types of media, both within Portugal and beyond - that Madeleine is not only dead, but that we, her parents, were somehow involved in concealing her body."
The decision was taken in a bid to prevent further publication of Mr Amaral's "deeply offensive" book The Truth of the Lie and his television documentary.
But Mr Amaral told Portuguese television his lawyers are working on the case and may take the McCanns and others to court for "defamation, slanderous denunciations and false statements".
"We will see who has spoken the truth in this case," he added.
The McCann's UK lawyer, Edward Smethurst, said their first step would be to apply for a gagging order at Lisbon's main civil court.
"There is no evidence that Madeleine is dead. Therefore not only is this book damaging and libellous, but it's also damaging the search for Madeleine," he said.
He was confident the injunction would be granted, he added.
The couple's statement continued: "The primary reason for our legal action is simple: to stop any negative effect that these absurd and deeply hurtful claims may be having on the ongoing search for Madeleine.
"We can no longer stand back and watch as Mr Amaral tries to convince the entire world that Madeleine is dead.
"Nor can we allow this blatant injustice to Madeleine, with its obvious risk of hindering our attempts to find her, to continue."
It said Mr Amaral's claims had brought "indescribable devastation" to the McCanns, compounding the "immense pain and anxiety" that they had endured since Madeleine's disappearance.
Until he was removed from the case, Mr Amaral had headed up the regional Policia Judiciaria (PJ) in Portimao.
His removal came after comments were published in a Portuguese paper, but police reportedly gave no reason for his departure.
At the time PJ's national director, Alipio Ribeiro, told journalists Mr Amaral's "commission of service has ceased".
Portuguese police placed "arguido" - or formal suspect - status on Kate and Gerry McCann in September 2007, but it was lifted in July 2008 when detectives stopped actively searching for Madeleine.
The Portuguese police have said they are no longer actively investigating the case.