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Meanwhile, a sexually motivated abduction is emerging as the main line of inquiry for police investigating Madeleine's disappearance, BBC correspondent Matthew Presland said.
Madeleine parents 'stay positive'
Other family members have spoken out against criticism of the police made in the Portuguese and British media.
Three-year-old Madeleine, of Rothley, Leicestershire, disappeared from an apartment in Praia da Luz six days ago.
The parents' statement, read out by Alex Woolfall, spokesman for the operator of the resort where the family were staying, said: "We are grateful to all of those currently taking part in the search for our daughter Madeleine.
The woman was said to be urging the girl to say "thank you" to staff, but the youngster had appeared reluctant.
British child-abduction experts have flown to Portugal to join in the hunt.
Madeleine's grandparents, Brian and Susan Healy, have spoken of the strain that her parents are under.
"They can pull it together when they have to, but obviously there are times when they are very distraught," she said.
Mrs Healy added that the inexperience of the Portuguese police possibly led to mistakes initially, but debating what went wrong "doesn't achieve anything".
"We just have to move on and just pray that because of the publicity, for which we're grateful, somebody will come forward."
The Anglican church in Praia da Luz held a prayer vigil for Madeleine.
"We all have deep fears and absolute hope," he said.
The BBC's Alix Kroeger said police in Portugal had released no new information about their inquires, but false alarms and speculation was rife.
Among rumours, one claimed an abandoned car was undergoing forensic testing, and another was that CCTV footage from a petrol station was being examined by police.
But none had proved accurate so far, said our correspondent.
Madeleine is believed to have been taken from her bed last Thursday evening while her parents were eating at a nearby restaurant.
They had been regularly checking on her and their two-year-old twins, Sean and Amelie, before she went missing.
Mr Healy said that people who criticised the parents for leaving the children are "misguided and have got it wrong".
Their comments came after the British ambassador to Portugal, John Buck, defended the police search.
He said he had been assured by Portuguese authorities that "everything possible" was being done to ensure the girl's safe return.
Portuguese police have also rejected local media claims that more effort has been put in than would have been made for a Portuguese child.
A Downing Street spokesman said these were difficult days for the family and for those trying to lead the investigation, and said help was being given wherever possible.
Mark Warner Holidays, operator of the resort, said it has received more than 400 messages of support for the McCanns from 20 countries.
An online appeal to help find Madeleine has also been set up.
The appeal, created by the Child Exploitation and Online Protection Centre and the Virtual Global Taskforce, is available in English, Portuguese and Spanish on www.ceop.gov.uk.
Crimestoppers have also set up an international number - +44 1883 731 336 - which people with information can call anonymously.
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