Prosecutors in the eastern Burgenland state, where the gruesome cargo was discovered, were seeking a "centralised investigation of the entire criminal procedure through the Hungarian justice system", spokesman Roland Koch told AFP.
The badly decomposing bodies of the 59 men, eight women and four children were found on August 27 inside an abandoned refrigerator truck on the A4 motorway, close to the Hungarian border.
Investigations revealed that the refugees - mostly from Syria, Iraq and Afghanistan - had been picked up at Hungary's border with Serbia and transported to Austria.
An autopsy showed they had most likely suffocated while still in Hungary.
The government there has taken a controversially hard-line stance against migration amid Europe's worst such crisis since World War II.
So far, six people have been detained in connection with the case, which sparked international revulsion and highlighted the plight of migrants and refugees putting their lives in the hands of human traffickers to reach Europe.
But Koch said Austrian police would drop an arrest warrant against one of the suspects, a 32-year-old detained in Bulgaria who was due to be extradited to Austria.
The man was no longer a suspect in the case, Koch confirmed.
Another five men, four Bulgarians and an Afghan, are under arrest in Hungary over the tragedy.
More than half of the refugees have now been identified, an official source said. Four of the victims were buried in a cemetery in Vienna on Wednesday.