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Scotland Yard detectives are separately trying to identify two fair-haired men - thought to be Dutch or German - who were seen "lurking around" the Praia da Luz apartment on the night of Madeleine McCann's disappearance.
TV appeals regarding the men will run in Holland and Germany, though not in Portugal.
One is of a man who was seen twice by the same witness near the flat where the McCanns were staying.
He was described as aged 30 to 35 and thin, with short hair, shaving spots on his face and wearing a black leather jacket. Another witness saw a similar-looking man in the resort.
Police say their presence close to the Ocean Club points to possible reconnaissance of the apartment complex.
Evidence gathered to rule out the sighting of a man and child previously thought to be Madeleine McCann and her abductor has been described as a "revelation" by police investigating the three-year-old's disappearance.
Detective Chief Inspector Andy Redwood told BBC's Crimewatch programme why the revision of the 9:15pm sighting in the timeline of the night of May 3 2007 has had such significance on the investigation.
The search for a man seen carrying a child at 10pm on the night Madeleine McCann disappeared has become detectives' main new line of inquiry after a key sighting from the original Portuguese investigation was ruled out.
Scotland Yard officers now say that a man seen carrying a child by Kate and Gerry McCanns' friend Jane Tanner was an innocent British holiday maker who they are "almost certain" was not Madeleine's abductor.
Instead the investigation has been re-directed to find another man with dark hair who was seen in Praia da Luz with a little girl in his arms around 45 minutes later on the evening of May 3 2007. A pair of e-fits of the man from two sightings were released earlier today.
The Metropolitan Police's Madeleine McCann investigation team has been inundated with calls from the public after they released a new e-fit in the search for her abductor.
An increasing interest in a 10pm sighting of a man carrying a child on the night Madeleine McCann disappeared has come after a "change of emphasis" in the timeline of her abduction, the Metropolitan Police have said.
Detective Chief Inspector Andy Redwood urged the man, who was seen by two people, to make himself known to police.
Police investigating the disappearance of Madeleine McCann have issued a more detailed description of a man who witnesses saw carrying a child away from the direction of the apartments on the night the three-year-old was taken.
Detective Chief Inspector Andy Redwood said it was "vital" they identify the man who was seen walking towards the beach area or the centre of the town at around 10:00pm on the night Madeleine was taken from a Praia da Luz holiday resort on 3 May 2007.
"The description of two different witnesses who saw him said he was a white man aged in his 30s with short brown hair, medium build, of medium height and clean-shaven," Detective Redwood said. "He was seen carrying a child aged 3-4 years old who had blonde hair and was possibly wearing pyjamas."
He added: “There may be an entirely innocent explanation of this man but we need to establish who he is to assist with our enquiries.”
Prime Minister David Cameron gave his support to the investigation into the disappearance of Madeleine McCann.
"I'm very pleased that Scotland Yard are doing this work. The Government has helped to fund the work that is being done.
"This was a crime that touched the heart of everyone in the country and everyone would like to see it resolved, so I hope Scotland Yard continue with their work and I wish them success."
Detectives investigating the disappearance of Madeleine McCann are asking for the public's help to identify a man who witnesses claim they saw carrying a blonde child in the Praia da Luz area on the night she went missing.
A former suspect in the inquiry into the disappearance of Madeleine McCann said he hoped the case was finally resolved.
Robert Murat, who was subsequently cleared, told ITV's Daybreak: "It's one thing I do hope and I have ever since 2007. I think it's something that needs to be dealt with.
"In my case there are still situations, for example on the internet, where you see stories of was he involved or wasn't he involved. So, having this situation resolved would resolve that situation too."
The Portuguese have "total apathy" towards a renewed campaign to find Madeleine McCann as they feel "the case is dead", an English journalist based in Portugal has told Daybreak.
"People are just not talking about it," Paul Luckman explained. "It's just not interested - the whole case is over as far as they are concerned.
Latest ITV News reports
Detectives have ruled out the key sighting that underpinned the original Madeleine McCann investigation and adopted a new focus in the hunt.
On the day she disappeared Madeleine McCann asked her parents a question: “Why didn’t you come when Sean and I cried last night?”