The parents of Madeleine McCann say they feel guilt about not being with her when she was abducted.
Kate and Gerry McCann told the BBC "no-one will ever feel as guilty as we do" after she disappeared from their apartment as they ate dinner nearby.
The couple said it was "every parent's worst nightmare", but that thousands of other people would have done the same.
Police say they are looking for a white man aged 35 to 40 who was seen in Praia da Luz on the night Madeleine vanished.
The couple said they loved their daughter "more than anyone could imagine" and still believed the "extroverted, vivacious and lively" little girl would be found safe and well.
"If anything really bad had happened we would have found her by now," Mr McCann said.
Clutching Madeleine's favourite toy, 'Cuddle Cat', her mother added: "We need to believe that she's coming back to us."
Before her disappearance, Mr McCann said the holiday had been "idyllic" and Madeleine was having fun with her brother and sister, Sean and Amelie, who are twins.
"She might look like Kate, but in terms of personality she is more of a McCann. She is very funny and often a little ringleader in nursery and with her friends," he said.
"She was running around shouting, 'Be a monster, be a monster' and we would chase her."
On the night Madeleine vanished, they were checking on her every half an hour and said they were "absolutely certain" from the first moment that she had not just wandered off.
They said the police were called within 10 minutes and the response from the staff at the resort had been "excellent".
There was criticism about the time taken by police to get searches under way and of the lack of information that could be given to the family under Portuguese law.
Mr McCann said it was "no secret" that the "information void" in the first 48 hours of the investigation was the "hardest thing for Kate and I to deal with".
"It took us back to the darkest places that we didn't want to do and ultimately doesn't help you.
"The worst feeling was helplessness and being completely out of control of anything in terms of getting Madeleine back."
Mrs McCann said: "The first 48 hours were incredibly difficult and we were almost non-functioning I'd say, but after that we got strength from somewhere."
The McCanns said "communication channels" had opened since then: "Certainly at the minute we are happy about how information is conveyed to us."
And they said it had helped "tremendously" when they began to take some control of publicity around the case.
'Dinner in your garden'
The couple said criticism of their decision to leave their children in the apartment while they ate had been "hard to deal with".
"No-one will ever feel as guilty as we do over the fact that we weren't with Madeleine at the time when she was abducted," Mr McCann said.
"Whether we were in the bedroom next door we would still feel as guilty."
He said the restaurant had a direct line of sight to the apartment and was "not dissimilar to having dinner in your garden".
And he insisted their half-hourly checks on the children were just as "rigorous" as any official babysitting service.
"If you thought for a moment that someone could abduct your child of course you would never have left them, but that was the furthest thing from our mind after what up until then was an idyllic holiday."
Mrs McCann said Sean and Amelie were handling their sister's disappearance very well.
"They do talk about Madeleine and Amelie has asked where she is. They will say, 'This is Madeleine's and that's Madeleine's'.
"They'll include her if they're saying, 'Who wants a biscuit?'"
And Mr McCann said the twins helped them carry on and be positive.
"If we had discovered all three of our children had gone we would not have had the same strength, resolution and determination to find Madeleine as Sean and Amelie give us.
"Life continues, but we need to bring Madeleine back as much for them, as for Madeleine, as for us," he added.
Mrs McCann said the couple had been working "very hard" doing all they could to get Madeleine back.
Both said they were touched by the support given by the public.
Gerry McCann with Madeleine and her sister Amelie
"People we don't know are doing do much to help," Mr McCann said.
He said the fighting fund which has raised almost £300,000 had allowed them to set up a "comprehensive legal team", but at present the family was happy to follow advice not to call in private investigators.
Mr McCann repeated the plea for anyone with information to come forward and to send any photographs of strangers in the resort to the police.
British police from the Child Exploitation and Online Protection Agency (Ceop) have so far received more than 500 images which they plan to cross-reference against a database of pictures of UK paedophiles and other criminals.
"We believe the public will hold the key. Someone knows something," Mr McCann added.
Any holidaymakers in Praia da Luz at the time can send their photos to Ceop via a website - www.madeleine.ceopupload.com.