German officials investigating a 43-year-old man over the death of Madeleine McCann, who disappeared in Portugal aged only three, believe she is dead. Her parents had said on Thursday that the announcement of a new suspect was a potentially highly significant development in the 13-year worldwide hunt for their daughter. “The public prosecutor’s office in Braunschweig is investigating a 43-year-old German national on suspicion of murder. From this you can see that we assume that the girl is dead,” Braunschweig state prosecutor Hans Christian Wolters said. Madeleine disappeared from her bedroom on May 3, 2007, during a family holiday in the Algarve while her parents were dining with friends nearby in the resort of Praia da Luz. British and German police appealed on Wednesday for information about a German child sex offender currently jailed in Germany who was 30 at the time of Madeleine's disappearance. "Kate and Gerry do feel it's potentially very significant," Clarence Mitchell, a spokesman for the family, told BBC radio. "They've never given up hope that she may still be found alive but they are realistic." "Whatever the outcome of this particular line of investigation may be, they do need to know what happened to their daughter to find peace and to bring whoever is responsible to justice," Mitchell said. Police want to speak to anyone who has relevant information about a 43-year-old man, whom they did not name, or the movements of two vehicles linked to him during the period around the girl's disappearance. Both cars, a Volkswagen camper van and a Jaguar, are now in the possession of German police. The man, German police said, lived in the Algarve from 1995 to 2007 – and for several years in a house near Praia da Luz – and burgled hotels and holiday flats as well as traded drugs. German police said the man had been "sentenced on numerous occasions to prison terms for sexual abuse of children in the past". They said they were treating the case as a suspected murder and had determined the method used to kill the missing girl. They did not believe the murder was premeditated.