Police in Portugal believe that Madeleine McCann may be in the hands of a kidnapper who has not issued a ransom demand because of the intense media coverage of her disappearance.

Detectives said the abductor may have "panicked" because of the worldwide response to the case of the missing child, who was taken from her bedroom in the resort of Praia da Luz a month ago.

In the first hint that the coverage of Madeleine's disappearance may have inadvertently hampered the investigation, Olegario Sousa, a spokesman for the Judicial Police, said: "Who would ask for money for the girl when her image is running around the world?"

Kate and Gerry McCann have said the family would pay any sum to get the four-year-old back.

"If we thought it would secure her safe return, we would sell our house, we would do anything to get our daughter back," Mr McCann said.

Meanwhile it was reported yesterday that the police investigation was refocusing on Morocco after a series of "significant" mobile phone conversations were picked up by the British Government's Communications Headquarters (GCHQ) in Cheltenham.

The calls - all in Arabic and made on a Spanish pay-as-you-go phone - were said to have referred to "the little blonde girl" and were made last week. They talked about Mr and Mrs McCann meeting the Pope.

Intelligence officers also picked up repeated references to a German man, and discussions about Morocco, Holland and Germany.

The Arab-speakers talked about ferry crossings from the Spanish port of Tarifa, three hours from Praia da Luz. There are regular crossings from Tarifa to Tangiers in Morocco.

Mr and Mrs McCann had not been officially briefed on the report. A source said: "They read it with interest but they are awaiting concrete developments from police rather than following every potential lead and continued speculation."

In a joint statement released yesterday, the parents said: "It is incredibly difficult not having Madeleine here. As every week becomes a month, we still believe she is out there and alive and we remain and determined that we will find her with everyone's help."

Portuguese police are pinning their hopes on the results of more than 200 DNA samples collected. They have discovered the DNA profile of a "stranger" in the bedroom where Madeleine was abducted on May 3. Sources said it was not that of Robert Murat, the formal suspect in the case.

Police are now cross checking it against all the friends who were holidaying with the McCanns in the Algarve and all staff at the Ocean Club complex in Praia da Luz where they stayed. The sample is also being sent to the UK to be run through the DNA criminal database.

The investigation by Portuguese police is thought to be one of the most expensive undertaken in the country.

Mr Sousa said: "Human life does not have a price and we will continue until we find Madeleine."