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McCann, then aged three, went missing from her bedroom at the Praia da Luz holiday resort in the Algarve region while her parents were dining with friends at a nearby restaurant, leading to a global search that gripped the world's media.
London police, who started a review of the case in 2011 and began their own investigation last year, said today they were looking for more information about 12 crimes committed in Portuguese holiday resorts.
In four cases between 2004 and 2006 a man sexually assaulted five white girls, aged between 7 and 10 years, in their beds, in three different Algarve resorts, police said. Two of the 12 offences were committed in Praia da Luz.
"We need to eliminate this man from our enquiries and ascertain whether these offences are linked to Madeleine's disappearance," Andy Redwood, senior investigating officer at London's Metropolitan Police Service, told a news briefing.
The man, described as being tanned with short, dark, unkempt hair, spoke English with a foreign accent and would appear early in the morning. In some incidents, he was disturbed and left.
"This an offender who has got a very, very unhealthy interest in young, white female children who he's attacking while they're on holiday in their beds," Redwood said.
"ALL OPTIONS" OPEN
Redwood said the new appeal for information on the man who carried out the attacks was just one of the "priority lines" of inquiry currently being pursued. British police are also in contact with their counterparts in Spain, Belgium, Jersey, Switzerland, Netherlands and Germany over the case.
British Prime Minister David Cameron ordered a new investigation by London police after the McCanns wrote to him three years ago saying neither British nor Portuguese authorities had done enough to try to find their daughter.
Redwood said McCann might have long been dead.
"There is always the potential that she didn't leave the apartment alive. What is important for us to do is consider all the options," he said.