The parents of missing Madeleine McCann have said they hope a renewed investigation into their daughter's disappearance could lead to her finally being found.

Kate and Gerry McCann said in a statement that they are "very pleased" that Portuguese authorities have decided to reopen the inquiry into the little girl's disappearance, which was shelved in 2008.

The couple said: "We are very pleased that 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.

"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."

The Metropolitan Police said today that the Portuguese investigation was being re-started as a result of new lines of inquiry emerging from an internal review.

It will run alongside Scotland Yard's ongoing investigation into Madeleine's disappearance, which has uncovered new leads that were detailed by officers last week.

Portuguese police had originally shelved their investigation in 2008, the year after Madeleine vanished, but supported the British-run inquiry.

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.

The new Portuguese lines of inquiry are separate from those being chased by the Met.

Mr Rowley said: "The meeting was very positive, and we and the Policia Judiciara have a shared determination to do everything possible to discover what happened to Madeleine.

"Colleagues in Portugal fully shared with us the developments in their review, and the fact that they were taking the significant step of applying for the investigation to be formally reopened.

"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.

"Today's development is good news. Combined with the formal reopening of the Portuguese investigation today, and our ever-closer working relationship, I believe that we have the best opportunity yet to finally understand what happened to Madeleine."

Yesterday Metropolitan Police Commissioner Sir Bernard Hogan-Howe defended the way Portuguese police handled the initial investigation into Madeleine's disappearance.

She vanished from a holiday apartment in Praia da Luz in May 2007 as her parents dined in a nearby tapas restaurant.

Sir Bernard said: ''I think sometimes these things at the beginning can be very difficult to deal with, you don't know exactly if the child has just wandered off. It can be very difficult to know if you've got a very serious crime.

''I'm sure for them that must have been a challenge. Anybody can go back after two, three, five, six years and say 'why didn't you do that'? That's easy in hindsight.

''We don't like it when it happens to the Met, and I'm certainly not going to do it to the Portuguese."

Refreshed appeals were made last week as part of the British investigation, with Mr Redwood appearing on television in the UK, Holland and Germany.

He revealed that 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 man - an 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.

"I think we've got very good collaboration between the Met and the Portuguese police and I think that is now starting to bear fruit.

"I hope it will enable a resolution of this terrible thing that happened to the McCann family, so that her parents are able to know finally what did happen to Madeleine."

Portuguese police said that a review team had been working since March 2011 to look back through information from the original investigation.

This process had uncovered potential new lines of inquiry.