They demanded a judicial inquiry and called on Portugal's justice minister to hunt down the source who leaked their official police statements to the media.
They want the country's police to investigate how the statements - given in the immediate aftermath of their daughter Madeleine's disappearance on May 3 last year - came to be leaked to a Spanish television channel.
Police in the couple's home county of Leicestershire have been informed and MP Stephen Dorrell called on the Foreign Office to raise the matter with the Portuguese authorities.
Police in Portugal supposedly operate in total secrecy and officers, suspects and even witnesses face jail if they speak out about ongoing investigations.
Madeleine: Missing for almost a year But behind the scenes, officers have briefed selected journalists with a series of sensationalised claims about the 11-month hunt for Madeleine.
The McCanns have endured wild allegations that they could have drugged their children or even dumped Madeleine's body during a publicity visit to Spain.
But they are especially furious about the timing of the latest leak, which derailed a planned trip to the European Parliament to call for an improved alert system for missing children.
The couple met advisers last night to discuss their response to the leak of the statements - in which it was revealed that Madeleine, then three, and her brother Sean, then two, were left crying in their holiday apartment the night before Madeleine disappeared.
A friend of the family said they would not lash out against the police in public.
'They are furious,' he added. 'They are resigned to the fact that they cannot stop this from happening, but their anger hasn't gone away. It's just that revenge is a dish best served cold.'
Mr McCann's sister Philomena said: 'The person responsible must be tracked down and disciplined for this latest leak.
'Gerry and Kate are yet again being victimised by the Portuguese police in the hope that the information will undermine and discredit them in the public's opinion.
'Publicising information about them is obviously aimed at deflecting attention from the fact that the police have not made any breakthroughs in their investigation.'
'The couple's spokesman Clarence Mitchell called for an end to the Portuguese police's series of 'smears' against the McCanns, who remain official suspects.
They have categorically denied any involvement in their daughter's disappearance.
Mr Mitchell said: 'It is brazen, it is shameless, it is cack-handed and it has got to stop.
'The Portuguese government must now get a grip on whatever element it is within the Portuguese police who has been responsible for these leaks, who is apparently doing it with impunity.
'Someone in the police doesn't want Kate and Gerry to widen the agenda for whatever reason.
'We know what they're up to - it's ridiculous and it must stop.'
He said the McCanns accepted they had made a huge mistake when they decided to leave their children alone in their Algarve holiday apartment while they ate dinner nearby with friends.
He said: 'They know that they got it wrong, they made a mistake and, boy, are they paying the price for that - in heartbreak and agony.'
The journalist who broke the story, Spanish crime reporter Nacho Abad, refused to reveal his sources or if the documents had come from a police officer.
But supporters of the McCanns said there were few other people who had access to the statements.
Mr Abad, of broadcaster Telecinco, said the timing of the leak was 'sheer coincidence' and not a deliberate attempt to cloud the McCanns' visit to Brussels.
He said it would be 'appalling' if police resources were wasted hunting for his source when they should be investigating Madeleine's disappearance.
'The McCanns can't be upset,' he added.
'So much speculation and so many lies have surrounded the Madeleine McCann case and we have told the truth.'
The row broke out as chief investigator Paulo Rebelo returned to Portugal for a crunch meeting with the public prosecutor who will decide if the McCanns will remain suspects.
Mr Rebelo had monitored British police interviews of the friends who were with the couple on the night Madeleine vanished - the so-called Tapas Seven.
- The journalist who broke the story, Spanish crime reporter Nacho Abad, refused to reveal his sources or if the documents had come from a police officer. But believes the McCann's are "totally innocent".
- I think that the person that leaked this will be tracked down and will be sacked and not before time, but will this be enough?
- Does more need to happen to get to the bottom of this shambolic farce of an investigation?
- Who was responsible for putting Goncalo Amaral in charge, despite him facing serious charges concerning another missing girl?
- Someone is responsible for a catalogue of errors concerning this case, who?
- Is something more sinister at play here?
- The McCann's have been quiet and not spoken out or given their side to this tragic event, while the Portuguese police have allegedly been leaking like a sieve - Do you think it is time that the McCann's ignored these archaic secrecy laws and actually gave their version of events?
- Do you think it polite, or do you think it was unnecessarily ignorant and rude that the chief PJ in charge of this case, failed to give the McCann's a call while the Pj were in the UK?