Animal rights organizations Animal Public and People for Animal Rights Germany filed charges after the zoo in the eastern German state of Saxony-Anhalt euthanized the three newborn cubs in early May.
"We can confirm the initial suspicions," Magdeburg chief prosecutor Silvia Niemann told German news agency DDP on Friday.
The zoo has said the zoo director Kai Perret decided to euthanize the cubs - offspring of Siberian tigress Kolina - in order to protect the purity of the species after consulting with a veterinarian and other zoo officials. A new testing method showed in February that the cubs' father, Toskan, is descended from Sumatran as well as Siberian tigers.
The zoo had planned to breed Kolina and Toskan since acquiring the pair in November 2006. Aborting the cubs would have been too risky for Kolina, Perret told DDP.
"We acted correctly and not in violation of the law," zoo spokeswoman Katrin Demco said on Friday, citing support from other zoos.
People for Animal Rights Germany said in a statement that concern over the purity of the breed was not sufficient grounds to kill the cubs.
"Those responsible at the Magdeburg Zoo deliberately bred these cubs without proper testing and then simply killed them," Kurt Simons, the group's chairman, said in a statement. "This is contrary to the intent of animal rights law and demonstrates the irresponsibility of the zookeepers."
The zoo froze the bodies of the cubs, two males and a female, and planned to deliver them to the University of Göttingen for academic use. The cubs' father, Taskan, was castrated.
The case is one of several in recent years in which Germany's zoos have butted heads with animal rights groups over the treatment of young animals.
Polar bear cub Knut became a star last year after an animal rights activist called for him to be euthanized after his mother rejected him. Knut was instead raised by hand, as was polar bear cub Snowflake in Nuremberg this year despite picketing from animal rights protesters at her media debut.
And in March, Berlin Zoo director Bernhard Blaszkiewitz admitted to being involved in the deaths of four wild cats when he headed the zoo's Tierpark facilities on the eastern outskirts of Berlin in 1991. Blaszkiewitz's admission came after allegations that hundreds of animals had disappeared the zoo under dubious circumstances.