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PRAIA DA LUZ, Portugal (AP) — German police said Thursday they presume a British girl who went missing in southern Portugal 13 years ago is dead, but Madeleine McCann’s parents still nurture hope their daughter will be found alive.

McCann was 3 at the time of her disappearance from an apartment while her family vacationed in the seaside town of Praia da Luz, in Portugal’s Algarve region, in 2007.

Police in Germany reported Wednesday they had identified a suspect, a 43-year-old German citizen currently imprisoned in his home country for a sexual crime. They did not name him.

The suspect spent numerous years in Portugal, including in Praia da Luz around the time of McCann’s disappearance, and has two previous convictions for “sexual contact with girls.”

Police in Portugal and the United Kingdom confirmed the new lead in the long-running case. They did not explain why, after so many years, suspicion had now fallen on the German man, who was registered in the German city of Braunschweig before he moved abroad..

Hans Christian Wolters, a prosecutor in Braunschweig, Germany, told reporters the man is being investigated on suspicion of murder.

“You can infer from that we assume the girl is dead,” Wolters said.

The development, though grim, raised hopes that the mystery surrounding the case might finally be resolved. Authorities have never before given so much detailed information about any suspect during the years of investigating the child’s disappearance, which received worldwide attention.

Her parents, Kate and Gerry McCann, said on their website www.findmadeleine.com that their hope of seeing their daughter again had not faded.

“All we have ever wanted is to find her, uncover the truth and bring those responsible to justice,” the couple, who live in the U.K., wrote. “We will never give up hope of finding Madeleine alive but whatever the outcome may be, we need to know as we need to find peace.”

Wolters, the prosecutor, wouldn’t give any other details of the suspect’s identity so as not to jeopardize the ongoing investigation.

German police said the suspect, described as white with short, blond hair and a slim build, was linked to a camper van seen in Portugal’s Algarve region in 2007.

Portuguese, British and German police appealed for the public’s help in building their case against the suspect, asking people if they remembered seeing him in or around Praia da Luz 13 years ago.

Her parents say Madeleine disappeared after they left her and her twin siblings asleep in their holiday complex while they had dinner with friends at a nearby restaurant.

Christian Hoppe of Germany’s Federal Criminal Police Office told German public broadcaster ZDF that police aren’t ruling out a sexual motive. He said whoever abducted the girl may have broken into the holiday apartment and then spontaneously committed the kidnapping.

Hoppe said the suspect in the McCann case lived between Lagos and nearby Praia da Luz, and was regularly in the Algarve region from 1995 to 2007.

The suspect’s description fits that of a 43-year-old man who was convicted in December of the 2005 rape of a 72-year-old American woman in her apartment in Portugal, local German newspaper Braunschweiger Zeitung reported.

The newspaper said the physical description provided by German authorities and other details match the defendant in the 2005 rape attack, who recently was linked to the case by DNA.

The suspect denied the charges during his trial and has appealed his conviction.

According to a copy of the rape verdict sent by the court in response to an AP question about the suspect’s December trial, his other convictions were for the sexual abuse of a child in 1994 and a case in 2016 when he was convicted of possessing child pornography. Other convictions include drug trafficking, burglary and weapons violations.

Police from Britain, Germany and Portugal asked for anyone to come forward if they had seen two vehicles linked to the suspect — a Volkswagen camper van and a Jaguar. They also sought information on two Portuguese phone numbers, including one believed to have been used by the suspect on the day of Madeleine’s disappearance.

Portuguese police declined to comment because the country’s judicial secrecy law forbids revealing details of open investigations.

In Praia da Luz on Thursday, local people wondered whether the riddle of what happened to Madeleine might finally be solved.

“It’s been so long to actually find someone that might be responsible for what happened so long ago,” said 20-year-old Daniel Westcottoy, who was at a nearby school when Madeleine disappeared. “It’s pretty shocking actually, but I think everybody wants to know what happened.”