"We have just found out that they left hospital yesterday with their parents. Then they vanished, and we think they went to Germany," spokesman David Furtner told AFP.
The two five-year-old girls and one six-year-old boy were among 26 migrants in the back of a van pulled over by police near the German border after a short chase shortly after 4:00 am on Friday morning.
Their rescue came a day after an abandoned truck containing 71 dead migrants including four children was found on a motorway in eastern Austria near the Hungarian border, provoking international revulsion.
The Austria Press Agency on Sunday quoted a doctor at the hospital in Braunau am Inn saying that although the children would have been kept in, "from a medical point they were not in danger any more."
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Like many migrants caught in Austria -- as well as the truck with the 71 bodies -- the Fiat Ducato with Spanish number plates driven by a Romanian began its journey in Hungary and was headed for Germany.
Since Hungary is in the visa-free Schengen zone, onwards travel is relatively easy.