MADELEINE McCann's parents have said the fact police have found no evidence relating to their missing daughter has reinforced their belief that she could still be alive.
Kate and Gerry McCann, who is originally from Glasgow, said they were very pleased with the significant activity that had taken place in Praia da Luz and that it was gratifying to know that a substantial amount of work will take place over the coming months.
However, locals in the area have described the probe as a "nuisance" that is killing tourist trade.
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Detectives found no evidence relating to the missing child during searches of three areas of land over the past 10 days, but have said more will be carried out "shortly".
In a statement, Mr and Mrs McCann said: "We are very pleased that significant activity has taken place in Praia da Luz over the last 10 days with police officers and support teams from the UK working closely with the Policia Judiciaria and the Guarda Nacional Republicana.
"We are further encouraged that, despite the intensive searches, no trace of Madeleine has been found and this reinforces our belief that she could still be alive.
"We have always wanted all reasonable lines of inquiry to be followed and it is gratifying to know a substantial amount of work will take place over the coming months with the close co-operation of the British and Portuguese authorities.
"We would like to thank all those involved for their efforts and the members of the public who have come forward with information."
Scotland Yard last night said there was "still a substantial amount of work yet to be completed in the coming weeks and months" and the recent activity was only the "first phase of this major investigation which has been agreed with the Portuguese".
The officers were believed to be flying home yesterday and today. It is not clear when they will return.
Their departure comes as residents and business owners in the Algarve resort spoke of their frustration at learning police activity is set to go on, with one telling British police to go home.
Yesterday, locals in the town suggested they should sue the British police for the loss of earnings they have incurred, with another claiming the investigation was damaging the resort.
Waiter Fernando Pereira said the timing of the searches, at the start of the tourist season was a "nuisance".
A local estate agent, who gave his name only as Pedro, said the probe was putting off potential buyers. He said: "What happened is nothing to do with the people of Praia da Luz but it will always be associated with Madeleine."
The force said the decision to search the horseshoe-shaped piece of scrubland close to the Ocean Club resort where Madeleine went missing aged three in May 2007, with the two sites investigated yesterday, was a specific result of the UK's investigation work to date.
As police prepared to search the second two areas, graffiti slurring the family and describing British police as "stupid" was scrawled on a nearby wall overnight.
A spokesman for Mr and Mrs McCann, from Leicestershire, declined to comment on the graffiti, which was written in large red letters in Portuguese.
The new operation in Portugal is only being carried out at the request of the British authorities after they submitted four International Letters of Request.
There have also been unconfirmed reports last week that Scotland Yard has been granted permission to question three suspects about the case.
The Portuguese have also reopened their inquiry into Madeleine's disappearance but, while they are working with the UK force, they have refused to set up an official joint investigation.