The child's parents, Glasgow-born Gerry McCann and his wife Kate, said they were pleased after Portuguese authorities announced plans to reopen the inquiry into the girl's disappearance after new lines of inquiry emerged.
The couple said: "We are very pleased the investigation to find our missing daughter Madeleine has been officially reopened in Portugal.
"We hope that this will finally lead to her being found and to the discovery of whoever is responsible for this crime."
Madeleine was three when she vanished from a holiday apartment in Praia da Luz on the Algarve in May 2007.
Portuguese police had originally shelved their investigation in 2008, but announced yesterday the case would be restarted after an internal review of the original inquiry.
A review team was instructed in March 2011 to sift through the information gathered and their work uncovered new lines of inquiry that are being dealt with separately to those being chased by Scotland Yard.
Mr and Mrs McCann added: "We once again urge any member of the public who may have information relating to Madeleine's abduction to contact the police in Portugal or the UK.
"Please be patient and respect the work of the police as they endeavour to find the answers we so desperately need.
"In particular we request that the media consider carefully Madeleine's safety and the integrity of the investigation in their reporting."
Detective Chief Inspector Andy Redwood, who is leading the Scotland Yard team, Assistant Commissioner Mark Rowley and Mr and Mrs McCann met officers in Lisbon last week to be briefed on the Portuguese case.
Mr Rowley said: "This is a welcome development, but both sides of the investigation are at relatively early stages, with much work remaining to be done.
"This new momentum is encouraging, but we still have a way to go and, as with all major investigations, not all lines of inquiry that look promising will yield results.
"The development is good news. Combined with the formal reopening of the Portuguese investigation today, and our ever-closer working relationship, I believe we have the best opportunity yet to finally understand what happened to Madeleine."
New appeals were made last week as part of the British investigation, with Mr Redwood appearing on television in the UK, the Netherlands and Germany.
He revealed his team had discounted a previous sighting by the McCanns' friend Jane Tanner, which was thought to be an abductor carrying Madeleine away and had been put at the centre of the Portuguese investigation.
His team managed to track down the innocent British holidaymaker and instead decided to focus on a second suspect who was also seen with a child in his arms.
Officers also said they would like to trace a number of fair-haired men who were seen near the apartment at the time, and are looking at a surge in burglaries in the area as well as bogus charity collectors.
An appeal is due to air on Irish television later this month.
Home Secretary Theresa May said: "The police have been working very closely with the Portuguese police and I think they've been developing the evidence and the leads and possibilities of leads that we've seen coming forward recently."