Mr Priebke, 81, was arrested in the southern Andean resort of San Carlos di Bariloche, where he had lived openly for 46 years until being traced to the town by the US television network, ABC.
He is wanted in connection with the reprisal killings in March 1944 of 335 Italians at the Ardeatine Caves near Rome.
Argentine federal judge Leonidas Moldes said Mr Priebke had been granted house arrest on medical grounds. 'The Italian authorities have 45 days to present documents formally requesting extradition,' he said. Mr Priebke says he fled Italy in 1948 with the help of the Vatican - a claim rejected by a leading Catholic historian.
Mr Priebke acknowledged in an ABC interview last week that he had been involved in the Ardeatine killings but said he regretted his part and had been following orders. The massacre, directed by SS Lieutenant-Colonel Herbert Kappler, was in reprisal for an Italian partisan bomb attack in which 33 German soldiers were killed. Mr Priebke says all the victims were Communist partisans. Jewish and Italian organisations maintain that the SS included Jews, common prisoners, women and teenagers to meet a quota of 10 Italians for every German killed by the bomb.
An Italian military tribunal shelved proceedings against Mr Priebke in 1948 when he disappeared from Italy without trace.
The former SS officer was quoted on Tuesday by the Italian newspaper La Repubblica as saying that he had escaped from a British prison camp in Rimini in 1946 and lived for two years in German-speaking north-east Italy.
'I couldn't leave with my own passport so I asked for help from the Vatican,' Mr Priebke told La Repubblica. 'It (the Vatican) got word to me through Bishop Alois Hudler that it was prepared to help me.' He said he travelled to Argentina on an Italian cargo ship with his wife and two sons, using Red Cross passports.
Father Robert Graham, an American Vatican-based Jesuit, said Hudler, a pro-Nazi Austrian bishop who died in 1962, had been banned from the Vatican several years before Mr Priebke's flight because of his support for Hitler and could not have influenced the Vatican in his favour.
Mr Priebke told La Repubblica he had personally shot one of the Ardeatine victims but had been following Kappler's orders. 'We were disgusted. We couldn't understand how a German could do something like that, but Kappler was inflexible,' Mr Priebke said.
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