As calls flooded in from all over Portugal from members of the public reporting possible sightings of Madeleine, whose grandmother is from Co Donegal, her distraught parents made a public appeal for the safe return of their eldest daughter.

"Words cannot describe the anguish and despair we are feeling as parents of our beautiful daughter Madeleine, " said her father Gerry McCann yesterday as he put his arm around his wife, Kate. "Please, if you have our Madeleine, let her come home to her mummy, daddy, brother and sister."

Madeleine disappeared sometime after 9pm on Thursday night from the room she was sharing with her twin siblings in the luxury Ocean Club complex in Praia da Luz. Her parents, Kate and Gerry McCann, both 38-year-old doctors from Rothey, Leicestershire were dining with friends some 40 yards away from their ground-floor apartment and were checking on their children every 30 minutes.

Madeleine was last seen by her father at 9.15pm that night. When Kate went to check on the children at 10pm, she found the shutter of the apartment window had been forced open and Madeleine was gone. Twoyear-old twins Amelie and Sean lay undisturbed in their cots and nothing else had been taken. It is believed the abductor may have been spying on the family and deliberately targeted the little girl.

As the search for Madeleine widened along the coast of the Algarve yesterday, her Irish grandmother, Ellen McCann, originally from Burtonport, Co Donegal, flew out to offer her support to her son and his wife. Originally Ellen Ferry, she moved to Glasgow as a young woman and met Gerry's father, John, there.

Guilhermino Encarnacao, director of the judicial police in the Faro region, told reporters yesterday that detectives had a suspect in mind and a sketch had been drawn up.

He refused to give any more details for fear of endangering Madeleine's life but said police were optimistic that the little girl was still alive and well. The McCanns had travelled to Praia da Luz in a party of nine adults and eight children for a week in the sunny Algarve. They were due to go home yesterday but instead family members, friends and police liaison officers travelled to Portugal to help them in their search.

"He is at his wit's end, " said Gerry's sister Philomena McCann yesterday. "You can hear his voice breaking. His wife is just. . . she can barely stand up. She can't sleep, she can't eat." Madeleine is their "little princess", she added.

When the alarm was raised on Thursday night, staff and residents of the resort immediately set up a search party but the McCanns have been critical of the initial reaction of the Portugeuse police, which they say was too slow.

Madeleine, who has blonde hair and blue eyes, was wearing just a pair of white pyjamas when she was taken. Described as a "happy-golucky little girl", her most distinguishing feature is that the pupil of her right eye runs into the iris. She is due to celebrate her fourth birthday on Saturday.

Police sniffer dogs followed Madeleine's scent to a nearby supermarket before it was lost. Police believe she was probably then taken by car, but they are still investigating a motive for the abduction.

Praia da Laz is a popular resort with Irish holidaymakers, with Budget Travel offering holidays to the neighbouring village of Lagos. Budget Travel spokesman Clem Walsh said yesterday that this was an unfortunate but isolated event and he didn't believe the abduction would prevent Irish visitors from travelling to the resort.

"Irish people are very sensible holidaymakers and in 30 years of business, we have never had such an incident, " he told the Sunday Tribune. "We would advise parents to exercise common sense when holidaying with children and to make use of the babysitting and creche services that are available in our family resorts. Children of that age should not be left alone at night."

Although the McCanns have been criticised for not availing of the babysitting service offered at the Ocean Club, friends of the couple were quick to point out how protective they are of their children.

"Gerry and Kate did not leave the children in danger and they could see the apartment from the restaurant, " said close friend Pat Perkins.

"You just don't expect something so awful to happen."

Gerry McCann is a consultant cardiologist at Glenfield Hospital in Leicester, while Kate is a GP. Staff at the hospital were said to be shocked at the news.

"Gerry is a popular and hardworking colleague, for whom we have great affection, " said cardiologist Doug Skehan yesterday. "We hope that Kate and Gerry have their daughter back very soon."