The family of missing three-year-old Madeleine McCann were clinging to hopes that she is alive last night despite confirmation police are now convinced she was abducted.

Detectives in the Algarve said they are hunting a "suspect" after evidence appeared to rule out the possibility that Madeleine had simply wondered off.

While Portugal's judicial police - the equivalent of Britain's CID - refused to give precise details of who they are hunting, they revealed that they believe Madeleine is still alive.

Hundreds of tourists, British expats and Portuguese residents today joined a search for her.

Madeleine went missing from her family's rented holiday apartment in the Algarve village of Praia Da Luz on Thursday night while her parents, Gerry and Kate, were eating dinner less than a minute's walk away.

The couple said they had been making regular trips back to the apartment from a tapas restaurant opposite to check on Madeleine and their two-year-old twin son and daughter.

Border checkpoints and airports in Portugal and Spain were placed on alert.

But Guilhermino Encarnacao, director of the Judicial Police in the Faro region, said detectives believe she could still be in the country - even still in the Algarve.

Her parents, who live in Leicester, are being supported by a team of British police who flew in yesterday as people travelled from up to an hour away to join the search for Madeleine.

Encarnacao made clear police are considering the possibility that she was abducted for sexual abuse.

But amid speculation that police may be hunting a known paedophile, Encarnacao refused to give details of the suspect. He would not even reveal whether the person is male or female, or if they are Portuguese, British or another nationality.

It was not clear whether this means that police are looking for a specific, named individual, or simply someone fitting a description.

Experts have put together a sketch of a suspect for police, but the image has not been released to the public for fear of endangering the youngster's life.

Encarnacao confirmed that among lines of inquiry police are investigating is a report that a young girl was spotted walking along a road with two people.

Local expats said that there had been a report of a couple spotted walking along a road outside the town with a child.

But he said calls had flooded in from all over Portugal with possible sightings.

The news that police think Madeleine may be alive brought comfort to her parents, who were said to be on an emotional rollercoaster.

Madeleine's great uncle, Brian Kennedy, said: "We fear the worst but we are hoping for the best."

The child's aunt, Philomena McCann, said the family was elated at the announcement.

"It's more than hope. It's a distinct feeling of elation," she said.

But she said the family is desperate for a breakthrough.

"It's really important to keep your emotions in check because the last couple of days have been like a rollercoaster," she said.

"It's great to have some hope but we need something to happen. We want her back."

She said Madeleine's parents had the support of family and friends but felt exhausted and helpless.

She added: "Kate and Gerry are doing their best. They've got their twins to look after as well, but they've got the support of their family.

"They're living on nervous energy just trying to look after each other and the kids, but at times it's just exhausting to be living on their nerves all the time and not to be reacting to things.

"It's very difficult because one of the biggest problems is that they get snippets of things, they're not hearing something properly and they've concerns about not being told what's going on. It's that helpless feeling again."

Friends said the family initially felt "left on their own" by police during the first terrifying night of the search.

But when he was asked about criticism of how police had handled the search, Encarnacao said that police were not alerted immediately as frantic holidaymakers mounted an initial search.

Mrs McCann's parents are among those who have flown out to be with the couple.

Yesterday, Dr McCann returned to the apartment where the family had been staying - now a crime scene - to retrieve a suitcase of belongings.

The couple, who had made a brief appearance before television cameras to plead directly to anyone holding their daughter to let her go, kept a low profile yesterday.

At one point they were seen walking hand-in-hand to the apartment where they are now staying after dropping off the twins with friends shortly before meeting British ambassador John Buck at the resort.