The 43-year-old German man, who has not been named, is now in prison.
The prosecutor's office in Braunschweig - a city in northwestern Germany - is carrying out the investigation because the suspect's last registered address before going overseas was in the region. He spent numerous years in Portugal and has two previous convictions for "sexual contact with girls". His statement was broadcast live on the BBC.
An investigation by British police has identified more than 600 people as being potentially significant.
Police have said that the man in question is white and in 2007 is believed to have had short blonde hair, possibly fair.
Her disappearance has been a huge and ongoing story in both the United Kingdom and Europe, with the latest Metropolitan Police investigation into her disappearance costing over £11 million ($13.8 million). They released pictures of a white and yellow Volkswagen camper van that they believe the suspect was using that summer and of a Jaguar auto that was once registered to the suspect.
The man transferred the Jaguar to someone else's name the day after she vanished.
"The police have publicly put out the number that he was on and the number he received the call through: they seem very interested in that call as guiding what he was doing that night".
"All we have ever wanted is to fight and uncover the truth and bring those responsible to justice, whatever the outcome may be they need to find peace as any parent would". "They have not given up hope of finding Madeleine alive, despite the length of time".
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There's also a new 10.25-inch infotainment system with pre-loaded maps and satellite-based voice-guided navigation. The centre console sits high, giving the driver and front passenger the feeling of sitting in an armchair.
"[Madeleine's parents] are realistic, they simply want to know what happened to their daughter" he added. She was taken from her bed while her parents dined with friends nearby.
German police said on Wednesday that while the exact sequence of events was still a subject of investigation, the suspect may have had a sexual motive but it is also possible that he had made a spontaneous decision to abduct McCann during a break-in of the apartment where she was sleeping.
It's always been believed that the little British girl was kidnapped from her holiday villa while her parents Kate and Gerry had dinner with friends nearby. A report came on the TV about the anniversary of Madeleine's disappearance and he said something to suggest that he knew what happened.
Madeleine McCann was three-years-old when she disappeared in 2007.
German law enforcement officers have not explained what led them to conclude the man was involved in Madeleine's disappearance or why they believe she is dead.
The day after Madeleine went missing, the suspect got the auto re-registered in Germany under someone else's name, although it is believed the vehicle was still in Portugal.
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.
Jim said he feels that the missing jigsaw pieces are finally coming together: "I'm really positive, more positive than I've been in 13 years and I really hope we're coming towards the end of this journey".