The defendants, Gerhard Sommer, Heinrich Sonntag and Alfred Schoneberg – all in their 80s - are being tried in absentia as they are also under investigation in Germany.
The case was adjourned until 29 June, which will give prosecutors more time to combine the case with that of three other former Nazis who participated in the atrocity.
"Italian and international public opinion is focusing great attention on this trial, which must ascertain the truth and those who are responsible for the Nazi massacre," said Marco Montemagni, a member of Tuscany's regional government.
On Tuesday, local schoolchildren in the seaside town of La Spezia, where the hearing took place, observed a minute's silence in memory of the victims, 120 of whom were children.
The massacre occurred just days before advancing British troops swooped in to the regional capital of Florence.
Survivors say hundreds of retreating Nazi troops surrounded the village of Sant'Anna di Stazzema and rounded up residents.
In a four-hour period, they shot 560 people, mostly women and children, before burning their bodies, using the pews from the local church as fuel.
Others were herded into closed spaces and basements and blown up with hand-grenades.
The case came to light in Italy only after prosecutors stumbled across witness statements that had remained sealed in a cupboard for nearly half a century.