Police in the Austrian state of Burgenland gave the first complete account of the deaths of the migrants inside the lorry.
Three men have been arrested by Hungarian police, including two Bulgarians who are believed to have driven the lorry.
"In a human trafficking organisation, these are the two lowest levels," said Hans Peter Doskozil, the Burgenland police chief. "Our investigation has to focus on the hard core."
The nationalities of those under arrest suggested that a "Bulgarian-Romanian trafficking organisation" had been responsible for smuggling the migrants, added Mr Doskozil at a press conference. The lorry is believed to have left Hungary in the early hours of Wednesday, as part of the "Western Balkans" route bringing fugitives to the European Union.
"One Syrian travel document was found inside the lorry," added Mr Doskozil. "As to whether they were all Syrians, it's too early to say."
Hundreds of miles south-east of where the lorry was found, thousands of migrants continued a daily struggle to enter Hungary from neighbouring Serbia. At one dusty border crossing, surrounded by maize fields, a 42-year-old Syrian woman fainted just moments after reaching Hungarian territory, having walked for the previous 12 hours with her family.
At the border post, consisting of four concrete posts in the middle of farmland, there was no medical aid, food or water - and no shelter. The woman's family poured water over her face in an attempt to revive her. Police were asked to call medical help, but instead a squad car arrived and took the woman, who said she came from the Syrian city of Aleppo, to a refugee registration camp.
"This is just unacceptable. You have people collapsing at the door of Europe without receiving any help. It's a desperate situation," said Babar Baloch, a spokesman for the UNHCR.
So far this year, more than 100,000 refugees and migrants have entered the EU via the "Western Balkans" route. Hungary has tried to reduce the flow by building a razor-wire barrier along its 110-mile border with Serbia. Surveying this obstacle, Mr Baloch said: "This is Fortress Europe coming into being. It's a reminder of the Iron Curtain. Can Europe really hide behind walls and fences when these desperate people need help?"
Scuffles and fights also broke out yesterday among more than 1,000 people at Greece's northern border with Macedonia as exhausted, thirsty migrants jostled to get into position to cross.