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Madeleine has been missing for more than three weeks
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Police searching for Madeleine McCann are starting to assess the response to their most detailed public appeal.
Detectives issued a description of a man seen on the night the four-year-old went missing in the resort of Praia Da Luz in the Algarve.
Officers said the man was "carrying a child or an object that could have been taken as a child".
Portuguese police went public with the appeal after pressure from the McCann family to move the investigation on.
BBC correspondent Steve Kingstone in the Algarve said it was the first time the police had given a detailed description of a man they wanted to question.
But it is not known how long detectives had known this information or whether they believed the man abducted Madeleine on 3 May, he added.
Witness description
The man is said to be white, 5ft 10in, medium build with short hair, and wearing a dark jacket, beige trousers and dark shoes.
At a news conference, Ch Insp Olegario de Sousa urged the man or anyone who had seen him to come forward.
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Madeleine with her father and brother Sean
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He said the description of the man was given by one witness involved in the case.
Dozens of possible sightings of Madeleine were still being investigated, but none had so far proved positive, Mr Sousa added.
The BBC's correspondent said police were publicly playing down the similarities between the man described and the only official suspect in the case, Robert Murat.
Mr Murat denies any involvement in Madeleine's disappearance.
A spokesman for Madeleine's parents, Kate and Gerry McCann, said they were pleased that there "appeared to be a new development".
'Safe resort'
On Friday the McCanns told the BBC of the guilt they felt at not being with their daughter when she was abducted.
They said they were experiencing "every parent's worst nightmare" and loved her "more than anyone could imagine".
Madeleine, from Rothley, Leicestershire, was abducted from her bed in the Algarve resort as her parents ate dinner at a nearby tapas restaurant.
The McCanns said criticism of them for leaving her in the bedroom was "hard to deal with", but insisted that thousands of other people would have done the same "in such a safe resort".