Police: We know who took Maddy

They are working on the theory she is being held near to the Algarve resort from where she was taken.

At a dramatic news conference, the officer leading the inquiry declared: "We have a prime suspect. There is a portrait sketch of the suspect, but I am not going to reveal it because it may put the girl's life in danger. We believe she is still alive."

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The announcement gave Madeleine's anguished parents Kate and Gerry renewed hope. It came as a colleague of her mother, a doctor, approached The Mail on Sunday offering a £100,000 reward.

"You never, in your wildest imagination, could ever think something as awful as this could happen,' said the fellow GP, who asked not to be named. "The reason I want to put up this reward is simply in the hope they get that little girl back."

The toddler vanished from her bed at the Ocean Club holiday resort in Praia da Luz three days ago while her parents dined in a restaurant 40 yards away. The couple told relatives they fear they were being watched in the hours before the kidnapping.

Guilhermino Encarnacao, director of the judicial police in the Faro region, hinted there may be a sexual motive. "Kidnapping is not just for money but can be for sexual abuse,' he said.

But his belief Madeleine is still alive and his disclosure that he has witnesses brought a delighted response from the girl's family.

Her aunt, Philomena McCann, said: "It's more than hope, it's a distinct feeling of elation. But it's important to keep your emotions in check because the last couple of days have been like a rollercoaster. It's great to have some hope but we need something to happen. We want her back."

Madeleine, who will be four on Saturday, was taken from her bed in the ground-floor apartment she was sharing with her parents between 9.30pm and 10pm on Thursday night.

Her parents had been checking every half hour on the toddler and her younger twin brother and sister, Sean and Amelia, who were sleeping in cots next to her.

When Mrs McCann checked on the children, she found the apartment door wide open, the window shutters jemmied wide and her daughter's bed empty. She ran screaming from the apartment, sparking a huge search involving 150 police, firefighters and Portuguese civil guard, along with villagers and guests at the Mark Warner Holiday complex, many of them British.

Philomena McCann said: "We have no evidence she was stolen to order but you get this gut feeling why one child should be taken and the others left. We think they were being watched and this was premeditated. Gerry is worried that may have happened.

"Some people may ask why they left the children alone in the apartment but it was locked and they had a full view of the front door and they were checking every half hour."

Around a dozen sniffer dogs joined the search and it is believed they followed Madeleine's scent to a supermarket 50 yards away. However the trail is believed to have gone cold from that point. CCTV cameras in the supermarket did not pick up any images of the girl or her abductors.

The 44-year-old married father who offered the reward is a partner in the same Leicestershire surgery as Madeleine's mother, but amassed a multi-million-pound fortune buying and selling property.

Yesterday he broke down in tears as he described a recent visit to Dublin when his own three-year-old niece went missing for 20 minutes. "The feeling was utter devastation and fear but thank God we found her,' he said. "It is unimaginable to understand what Kate and Gerry are going through right now.

"I am not a close friend of Kate's, and I haven't spoken to her since this happened. Money isn't an issue to me, it is the hope they get Madeleine back."

Kate and Gerry, a cardiologist, were yesterday spotted walking in silence through the complex. Mrs McCann was still gripping tightly on Madeleine's favourite teddy bear, as she has since her daughter was taken.

The resort's open layout meant her abductor would have easily been able to watch Madeleine and her parents. One holiday rep said: "Young children are everywhere, and can easily be seen from the roads outside. There are fences, but anyone can be observed very easily. Security has never been a huge issue, however, as we have not had any great problems before."

Police have sealed off the three-storey block and checked the McCanns' apartment for fingerprints. All airports, ports and border posts have been alerted. However, the helicopters initially used in the search were quiet yesterday, and locals said there had not yet been a house-to-house search.

Mr Encarnacao angrily denied reports in the Portuguese Press that the police had initially treated statements given by Madeleine's parents with some scepticism.

He said police responded within 15 minutes and added: "I have 150 men looking for the girl. At first it was just a missing girl case. Now I can assure you it was a kidnapping. We have evidence of this. Yes, we believe she is still alive and still in Portugal. We do have witnesses. They have given evidence but I can't reveal much more."

The McCanns, who have been married eight years and recently moved into a £600,000 detached house in Rothley, Leicestershire, were on holiday with a group of colleagues and their families, paying around £1,600 for a week.

In the evenings, Mark Warner offers a creche and individual baby-sitters, but the McCanns, both 38, chose not to use either.

• If you have information about Maddy's whereabouts, call The Mail on Sunday newsdesk on 020 7938 7041.