BERLIN — Austrian authorities have arrested three Afghans as suspects in the rape and killing of a 13-year-old girl, a crime that has prompted strong condemnation and tough talk from the country's leader on crimes committed by migrants.

The girl's body was found next to a tree in Vienna's Donaustadt district on Saturday. Two Afghan youths, aged 16 and 18, were arrested as suspects on Monday. Both were asylum-seekers; the elder had had his protected status revoked as a result of three convictions that included one for robbery.

Police said Thursday that a third man, a 23-year-old Afghan, was arrested in Vienna on Wednesday evening on suspicion of involvement.

Officials have said that the victim knew the first two suspects and had voluntarily accompanied them to the 18-year-old's apartment. There, according to Vienna police chief Gerhard Puerstl, she was given drugs and "crimes against the sexual integrity" of the girl were committed.

Police say the elder of the two has denied having anything to do with the killing, while the younger hasn't yet said anything.

Chancellor Sebastian Kurz promised on Tuesday that authorities will ensure the perpetrators are "punished with the full force of the law."

"I find it intolerable for people come to us, say they are seeking protection and then commit cruel, barbaric crimes in Austria," he said.

"Politically, this means for me that we will stick to our consistent line," said Kurz, who has long taken a tough approach to migration issues. "With me, there will definitely never be a halt to deportations to Afghanistan or a watering-down of asylum laws toward asylum-seekers who commit crimes."