A 13-year-old Russian-German girl has admitted making up a story about being kidnapped and raped by migrants in a case that triggered a furore in Germany and briefly embroiled Berlin police in a spat with the Kremlin, state prosecutors said.

The parents of the teenager, named only as Lisa, reported her missing on 11 January after she failed to appear at school in the Marzahn district of the capital. She reappeared 30 hours later with injuries on her face, and told her parents she had been attacked by men of Middle Eastern or north African appearance. News of the incident spread on social media, sparking outrage among Berlin’s Russian-German community.

But when she was questioned by trained specialists three days later “she immediately admitted that the story of the rape was not true”, said the spokesman for the state prosecutor, Martin Steltner.

He said the teenager had been scared of going home after the school had contacted her parents over an incident at school.

Yet the allegations caused uproar in Berlin, particularly after reports of mass sexual assaults allegedly carried out by migrants in Cologne. A Russian-German community group staged a protest, supported by the Pegida-related Bärgida movement. The far-right National Democratic party also demonstrated in Marzahn.

The mood was exacerbated by a report on Russian state TV, in which the girl’s relatives claimed her allegations were not being investigated.

The Russian foreign minister, Sergei Lavrov, also weighed in to criticise the Berlin authorities. “The news that she disappeared was kept secret for a very long time,” he told a press conference, blaming “political correctness”.

Analysis of the teenager’s mobile phone records showed she had spent the night with a friend, who is not being treated as a suspect.

Her mother told Der Spiegel magazine on Sunday that Lisa was “doing very badly” and was having treatment in a psychiatric ward.