Police have told the parents of Madeleine McCann that they have received a “credible call” from a man claiming to know what happened to their daughter after her abduction 36 days ago.

Kate and Gerry McCann were asked if they were prepared to speak to the man after he told police that he wanted to talk to them. The couple hoped that the call was the breakthrough they have been praying for in the five weeks since their daughter, now aged 4, disappeared from an Algarve holiday apartment.

The call, believed to have been made to police in Spain, was traced to an unregistered pay-as-you-go phone, apparently from outside Europe.

Information provided by the man on Wednesday afternoon convinced British police, who are liaising with the Portuguese-led inquiry, that it was necessary to inform the McCanns immediately and to ask them to speak to the caller. It is not known what information convinced detectives that the caller was credible. The couple, from Rothley, Leicestershire, were contacted as they prepared to travel from meetings in Berlin to Tempelhof airport in the German capital for a private flight to Amsterdam.

British police liaison officers advised them that the source might try to make contact and that they should delay their flight. Frantic efforts followed to try to re-establish contact as the McCanns waited for three hours at the British Embassy in Berlin. A contingency plan was drawn up in which the McCanns would speak directly to the man. It involved them flying to Britain, where they were to be met by advisers to oversee talks. But when efforts to re-establish contact with the caller failed, the McCanns were advised to proceed to Amsterdam. They took off three hours later than planned.

A British police source said: “There was a possibility of a new line of communication. The importance of this line of inquiry is still being assessed and attempts to re-establish contact are continuing.”

Mr McCann used his internet blog yesterday to suggest that the couple no longer believed that the call was significant. “We diverted to the Embassy in Berlin but it turned out to be nothing of interest,” he wrote on www.findmadeleine.com. The Spanish Interior Ministry denied that anyone had called with information. Portuguese police refused to comment.

The McCanns were still said to be ready to talk directly to the man if contact could be re-established. Mr McCann said on Wednesday that he believed a single telephone call could return Madeleine home.

“Somebody can help us find Madeleine,” he said. “It is one telephone call — either a location or a name and that is what we are appealing for.” He had said it was difficult dealing with hundreds of claims from people who claimed to know where Madeleine was. Most are from clairvoyants or people who have had “visions”. One claim made in an e-mail was traced to a Hampshire schoolboy who has learning difficulties.

The McCanns came to the end of the European section of their campaign to promote their search yesterday. Mr McCann said they had targeted countries with large numbers of tourists in the Algarve: “We are not selling a book, we are not pop stars, we have come here for a very specific reason.”