Portuguese police say the German evidence against the new suspect in the Madeleine McCann case is “significant”.
A senior police source also told the BBC they were keen to cooperate in the investigation into the disappearance of the British girl in Portugal in 2007.
The new suspect is a 43-year-old German man, named in reports as Christian B, who is in prison in Germany.
He was revealed as the main suspect earlier this month, as German and UK police made a fresh appeal for help.
The convicted paedophile is believed to have been in the area where Madeleine, aged three, was last seen while on holiday in Portugal.
A senior Portuguese police source, who has seen the German evidence against Christian B, has told the BBC it is “very important” and “significant”.
The source also rejected criticism that their procedures were slow, amid reports that the German authorities have privately been critical of their Portuguese counterparts.
Another source close to the investigation said Portuguese police accepted that Christian B was now a suspect.
Asked whether they had access to his previous convictions for child sexual offences at the time of Madeleine’s disappearance, he said it was important not to judge the past with the benefit of hindsight, and that police systems since then had changed.
Some of those who knew the German suspect during his time in Portugal have criticised the investigation as “very slow”, telling the BBC that they were only approached by police – either British or Portuguese – in the past year or two.
Several people remembered Christian B as angry and untrustworthy, with one neighbour saying he squatted in a nearby house without paying rent, and left it “ransacked” in a terrible state when he departed, two years before Madeleine’s disappearance.
By BBC news correspondent Lucy Williamson, in Praia da Luz
When German police – newcomers to the Madeleine McCann investigation – announced they had evidence that indicated the toddler was dead, it seemed to get a cautious response from their Portuguese and British counterparts.
British police stuck to their line that it was a “missing person inquiry”, and the impression from Portuguese media was that their own tight-lipped authorities were staying open-minded.
This first-hand confirmation from a senior Portuguese police source that the German evidence is “very important” and “significant” is a sign of how seriously this new development is being taken there.
There’s been plenty of mutual recrimination between the British and Portuguese forces in the 13 years since Madeleine McCann vanished from her family’s holiday apartment.
Now a third country has entered the quest for answers.
Awkward? Maybe. But the German evidence, it seems, is convincing enough for the Portuguese police to signal their support.
After living for so long under the pressure of unanswered questions, they won’t want to be left out of a development that might promise some answers.
German prosecutors have previously said they have evidence that leads them to believe Christian B killed Madeleine, but it wasn’t strong enough to take him to court.
Police say the suspect was regularly living in the Algarve in Portugal between 1995 and 2007 and had jobs in the area, including in catering, but also committed burglaries in hotels and dealt drugs.
The suspect is currently serving a jail term in Kiel, Schleswig-Holstein, for drug-dealing, having been extradited from Portugal in July 2017.
He is believed to have been in the Praia da Luz area in May 2007, when Madeleine went missing while on a family holiday with her parents and siblings.
In December 2019, the man was sentenced to seven years for raping a 72-year-old American woman in the same Portuguese resort in 2005.
The Metropolitan Police, who are working with their German and Portuguese counterparts, have said the case remained a “missing persons” investigation in the UK because there was no “definitive evidence” as to whether Madeleine was alive or not.
Madeleine went missing shortly before her fourth birthday from an apartment in Praia da Luz, while her parents, Kate and Gerry McCann, were with friends at a nearby tapas bar.
Her disappearance sparked a huge and costly police hunt across much of Europe – the most recent Met Police investigation, which began in 2011, has cost more than £11m.