Kate and Gerry McCann sued Goncalo Amaral over his 2008 book “The Truth of the Lie,” in which he accused the couple of concealing the body of their daughter after she died accidentally.

In April 2015, Amaral was ordered to pay the parents 250,000 euros ($284,000) each in damages, plus interest in excess of 100,000 euros.

The couple plan to challenge the latest ruling, which was issued last Thursday by the Lisbon appeals court, their lawyer Isabel Duarte said.

The court ruled that Amaral had exercised “legitimate freedom of expression” and that the McCanns had to accept limits on their privacy after they had launched an international media campaign to find their daughter, TVI television reported.

Madeleine disappeared from her room on May 3, 2007, just days before her fourth birthday, in the small seaside resort of Praia da Luz in southern Portugal where the family were on vacation.

After 14 months of controversial investigations — which saw Madeleine’s parents investigated and Amaral sacked — Portuguese police closed the case in 2008 before reopening it five years later.

British police opened their own inquiry in July 2013, but on-site excavations in Praia da Luz yielded no evidence and Scotland Yard has since sharply reduced the number of investigators working on the case.