Madeleine McCann's parents are "absolutely delighted" with the "overwhelming" response to a fresh appeal for information about her disappearance, they have said.
In a statement, Kate and Gerry McCann said they are "genuinely hopefully" that one or more of the responses to last night's BBC Crimewatch appeal would lead to a major breakthrough in the investigation.
Police today said they have received more than 730 calls and 212 emails in response to last night's appeal, and detectives are now working through them.
In a statement issued through their spokesman, Kate and Gerry McCann said: "We are absolutely delighted with the overwhelming public response to Crimewatch, which was broadcast last night.
"We know that the public desperately want to help the search for Madeleine.
"We are genuinely hopeful that one of more of these responses will lead to a major breakthrough in the investigation."
They added: "If anyone was in Praia da Luz around the time of Madeleine's abduction and has not spoken to the Metropolitan Police, or if they know who any of the e-fits might be, please have the courage to come forward and speak to the police in confidence."
Earlier, Crimewatch editor Joe Mather described the response to the programme as "truly unprecedented", and said some callers had given the same name for a man spotted carrying a child towards the beach in Praia da Luz.
He said there were lots of calls from British people in the town around the time of Madeleine's disappearance who had never previously spoken to police, telling BBC Radio 4's Today programme: "They received several names for the key 10pm sighting, the sighting of a man carrying a child towards the beach.
"Several different names but also several callers mentioned the same name for that man."
Senior investigating officer Detective Chief Inspector Andy Redwood is repeating the appeal tonight in Holland on a programme called Opsporing Verzocht, and in Germany tomorrow night on Aktenzeichen XY...ungelost, he said today.
During last night's show, two new e-fits of a man were broadcast, while police said they had effectively ruled out a previous key sighting of a different man carrying a little girl - suggesting Madeleine may have been taken closer to 10pm that night.
Viewers were shown two images of a dark-haired man, based on descriptions from two witnesses who were staying in Praia da Luz when the three-year-old went missing.
Mr Redwood said during the show that two independent callers had put forward the same name for the man and another caller gave a name of a man who was known to be in Portugal at the time of Madeleine's disappearance.
Witnesses described the man in the new e-fits as white, aged between 20-40, with short brown hair, of medium build, medium height and clean-shaven.
While police appealed for information on that suspect, officers now say that a man seen carrying a child by the McCanns' friend Jane Tanner was an innocent British holidaymaker.
Mr Redwood said: "Our focus in terms of understanding what happened on the night of May 3 has now given us a shift of emphasis. We are almost certain that the man seen by Jane Tanner is not Madeleine's abductor.
"It takes us through to a position at 10pm when we see another man who is walking towards the ocean, close by to the apartment, with a young child in his arms.
"This child is described as being about three to four years of age with blonde hair, possibly wearing pyjamas, and the man is a white man with dark hair."
Investigators are also trying to identify mysterious fair-haired men seen "lurking around" the apartment at the time who could be Dutch or German.
Two e-fits of the fair-haired men have been released.
One is of a man seen twice by the same witness near the flat where the McCanns were staying. He was 30 to 35, thin, with short hair, shaving spots on his face and was wearing a black leather jacket. Another witness saw a similar-looking man in the resort.
Police are also looking at a spate of break-ins in the area, one of which happened in the same week a year before Madeleine went missing, where a man got into a flat where young children were sleeping.
Other lines of inquiry are bogus charity collectors operating in the area at the time, and a spate of burglaries that peaked in the month Madeleine went missing.
On the day that Madeleine disappeared, there were four occasions where bogus charity collectors targeted properties in the area.
There are also two e-fits of Portuguese men - one aged 40 to 45, who knocked on the door of the apartment where the McCanns were to stay on April 25 or 26 between 2.30pm and 3pm, saying that he was a charity collector.
The other, aged 25 to 30, approached a property on the Rua do Ramalhete, near the Ocean Club, at around 4pm on May 3.
A reward of up to £20,000 is being offered for information leading to the identification, arrest and prosecution of those responsible for Madeleine's abduction.