A kidnapper may have snatched Madeleine McCann with the intention of demanding a ransom, it has emerged.

The enormous amount of publicity about the missing four-year-old might have panicked the abductor into making no contact, police said.

The theory raises the possibility that a kidnapper may be keeping Madeleine prisoner until media attention subsides, making it safe to ask for money.

Kate and Gerry McCann made it clear they would 'do anything' to get their little girl back safely - and would not hesitate to sell their £800,000 home in Leicestershire to raise money for any ransom.

The possibility of an abduction for money was canvassed in detail by Portuguese police for the first time in public yesterday.

Chief Inspector Olegario Sousa said: "We continue to investigate the possibility that whoever took this child could have done it for money, and hasn't asked for a ransom because they've panicked with the headlines the case has generated.

"Who would dare ask for money for this child when her image is going around the world?"

He added: "A kidnapper could easily have a child hidden, possibly close by."

Madeleine disappeared on May 3 from the McCanns' rented holiday apartment in the Algarve resort of Praia da Luz.

They are convinced she was snatched from her bed by an abductor - and that a witness who saw a man carrying away a child in a blanket that night was their little girl in the clutches of her kidnapper.

Police called off their local search after only several days, and have since admitted that they did not enter locked apartments and buildings for which they could not find keyholders.

This week many of those holiday homes will be opened up to tourists for the first time this season.

It presented a slim strand of hope that Madeleine - or at least some trace of her - could be found if one of the empty flats had been used to incarcerate her.

Meanwhile police all over the world are on the alert for any contact with an abductor or blackmailer but have so far had none.

In Portugal, detectives are still ploughing through thousands of emails, letters and phone calls, some from so-called psychics, and many offering alleged locations where Madeleine is said to be hidden.

Officers admitted they had to investigate all the leads in case one turns out to be from a kidnapper offering coded clues.

However Ch Insp Sousa said other scenarios were still being investigated, including the 'most terrible' possibility that Madeleine had been abducted by a paedophile ring for use in child pornography films.

But he warned that experts were monitoring all such images 'microscopically' for any glimpse of Madeleine - and that her high profile would make it difficult or impossible to distribute the films.

Yesterday marked one month since Madeleine disappeared. The McCanns temporarily put the painful milestone to one side by attending Sunday Mass at Our Lady of the Light Roman Catholic church, which overlooks the ocean at Praia da Luz.

It has been their constant solace during the search for Madeleine but yesterday, the torment all but overcame them.

Dr McCann, a 38-year-old Leicestershire GP, wept openly after she and a young Portuguese girl exchanged kisses during a Sign of the Peace ceremony that formed part of the service.

Mr McCann, a 38-year-old consultant cardiologist, steadied her by putting his arm around her and allowing her to bury her head in his shoulder.

Kate, who was clutching Madeleine's Cuddle Cat toy and a copy of one of Madeleine's favourite books, We're Going on a Bear Hunt, eventually composed herself.

Later, in a statement that gave a brief insight into their four-week agony of uncertainty, the couple said: "It is incredibly difficult not having Madeleine here.

"As every day, every week, becomes a month, we still believe she is out there and alive and we remain positive and determined that we will find her soon with everyone's help.

"We do realise it is just a phone call that we need. We just want her home."