Kate and Gerry McCann refused to rule out taking legal action against the Portuguese authorities for wrongly making them suspects in their daughter Madeleine's disappearance.
Over the coming weeks the couple's lawyers will examine the police case files for unexplored leads to search for the little girl - and to judge whether they should press charges.
The McCanns, from Rothley, Leicestershire, vowed to continue looking for Madeleine after the Portuguese investigation was shelved on Monday.
The couple welcomed prosecutors' decision to lift their status as "arguidos", or formal suspects, but said they had no cause for celebration.
Her voice breaking with emotion, Mrs McCann said: "It is hard to describe how utterly despairing it was to be named arguidos and subsequently portrayed in the media as suspects in our own daughter's abduction.
"It has been equally devastating to witness the detrimental effect this status has had on the search for Madeleine."
After an exhaustive investigation lasting more than 14 months, Portuguese prosecutors announced on Monday that they had no evidence that the three suspects in the case committed any crimes.
As a result they shelved the case and lifted the arguido status of the McCanns and Algarve resident Robert Murat.
The inquiry can be reopened if credible new evidence comes to light, the Portuguese attorney-general's office said.
The McCanns' lawyers are to be given access to the police files this week, their spokesman Clarence Mitchell said.
