"The executions were dreadful - for me and my colleagues - but it was impossible to refuse to carry them out," a frail-looking Priebke says in the video message released on Thursday by his lawyer Paolo Giachini.
Priebke died under house arrest in Rome last week, aged 100.
"It was an order from (Adolf) Hitler. Those who refused to carry it out were to line up with the victims to be shot," claimed Priebke, who appears sitting at a desk wearing a blue shirt and sleeveless navy jacket with a bookshelf behind him.
In the video, entitled 'Victor's Justice', Priebke speaks fluently in Italian with a strong German accent.
Repeating his defence at his war crimes trial, Priebke claimed he and fellow SS officers were only carrying out orders, a defence which has been ruled invalid ever since the Nuremberg trials. He never repented the crime.
In 1998, Priebke was convicted by an Italian military court of overseeing Rome's notorious Ardeatine Caves massacre, Italy's worst World War II atrocity ordered by the Nazis after 33 German soldiers were killed in the capital in an ambush by resistance fighters.
"The Communist-organised partisans organised the attack, believing it would inspire the local population to rebel against the German occupation," Priebke says in the video.
In the attack, resistance fighters detonated a bomb hidden in a rubbish cart as a column of German soldiers was passing down Rome's Via Rasella March 23, 1944, prompting the Nazis to round up 335 civilians, including 75 Jews, for execution.
In the reprisal, Priebke, fellow SS officer Karl Hass and their soldiers systematically executed each captive with a shot in the back of the head in an alcohol-fuelled killing spree that lasted many hours.
The German soldiers were mainly inexperienced and some of the victims' heads were blown off while others were not killed outright and crawled into corners of the caves to die of their injuries.
A number of victims may have survived until they were buried under tonnes of rock debris when the Germans then tried to hide their crime by dynamiting the entrance to the caves on Rome's outskirts. The caves are now a memorial.
The bodies of the victims remained inside the caves for over a year until after the Italian capital was liberated by the Allies June 4, 1944.
Priebke's reputation as an international pariah was cemented after Argentina, where he lived for nearly 50 years after the war, refused to accept his body for burial and a planned funeral in a town near Rome was stopped on Tuesday after protests.
His body was believed to be at a military airport on Friday, outside Rome as negotiations continued between Rome and Berlin over its possible repatriation to Germany for burial at his family's request.
The Vatican banned a funeral in any church in Rome and the city's mayor refused to allow him to be buried there, amid fears his grave would become a neo-Nazi shrine.