"We know he was in the resort on the night, about an hour before Madeleine was last seen about 9pm.
"He took a phone call on his Portuguese mobile from another Portuguese mobile. The call lasted half an hour.
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He lived in a ramshackle old farm building which sits on a remote hillside along a footpath that runs from above the beach where Madeleine and her family played during their week's holiday in 2007.
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DCI Cranwell released details of two mobile phone numbers.
The first, (+351) 912 730 680, is believed to have been used by the suspect and received a call from another Portuguese mobile, (+351) 916 510 683, while in the Praia da Luz area, starting at 7.32pm and ending at 8.02pm on the night of 3 May 2007.
The caller, who is not thought to have been in the Praia da Luz area, is not being treated as a suspect, but is said to be a "key witness".
Madeleine McCann: Jailed German paedophile at centre of new police inquiry
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The new chief suspect in the McCann case, who has not been named, was jailed for seven years
last December for a brutal sex attack carried out in Praia da Luz just 18 months before the three-year-old was snatched from her bed.
The German national was tried and convicted in Germany for the rape of a 72-year-old American woman in Portugal in September 2005, according to
Braunschweiger Zeitung, the newspaper for the central German city of Braunschweig. His trial heard he planned the sex attack having broken into the victim's house with a rope to tie her up. She was blindfolded and gagged before being raped and robbed.
The man is just a year into his seven-year jail term for the crime - but is appealing claiming his extradition. He is reportedly already in prison serving an even longer prison sentence for a crime that has not been revealed.
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There are concerns that Germany's strict privacy laws, which allow the suspect anonymity, could hamper the investigation because potential witnesses aren't being given his identity.
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They think the man - who has also got previous convictions for sex crimes against girls - made money dealing drugs and burgling holiday homes and that could be how he chanced upon Maddie.
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The attack on the American pensioner took place in Praia da Luz, 18 months before Maddie vanished from the same resort town. It was unclear this morning why the man, who was extradited to Germany from Portugal, had not faced trial in Portugal for the offence.
German law prevents police from naming even convicted criminals – so the McCann suspect remained anonymous even as he was jailed last year.
Breakthrough in hunt for Madeleine McCann as German suspect identified