Scotland Yard says it has completed a two-year review of the case and identified 38 people of interest, including 12 UK nationals.
Madeleine was just three years old when she disappeared from the family's Praia da Luz vacation apartment in 2007, while her parents, Kate and Gerry McCann, dined nearby with friends. She would be 10 years old now.
Detective Chief Inspector Andy Redwood said he was in a "unique position" to analyze the information from new witness interviews, with the aid of seven private detective firms in the UK and Portugal.
"That has given us the ability to see this case with fresh eyes, and through that bring out new, genuinely new, lines of inquiry," Redwood said. "And I'm hopeful when we pursue those lines of inquiry that we will be able to bring some sort of resolution."
"Whether we will be able to solve it is a different issue, but I hope that we will be able to have the ability to move the investigation on," Redwood said. "I believe critically that this is an important moment for Madeleine. It is the culmination of that unique piece of work and it is a great opportunity which we intend to exploit to the full."
The 12 British persons of interest were in Portugal at the time of Madeleine's disappearance, Redwood said.
While Portuguese investigators have officially closed the case there, Scotland Yard said they have backed the UK-based investigation.
"Over the last two years what the review has told me is that there is no clear definitive proof that Madeleine McCann is dead," Redwood said. "So on that basis I still genuinely believe that there is a possibility that she is alive."