The family of Australian teenager Max Meyer, who was killed in an avalanche in Austria, has spoken about the “profoundly difficult” time after losing their son.

The teenager and his parents issued a call for help after getting stuck in deep snow in a narrow valley between two main runs at St Anton resort in Tyrol last Wednesday. They were advised by the ski patrol to stay where they were.

“At that point in time we were uninjured, and in no immediate danger,” Thomas Meyer and Julie Schatz said in a statement on Monday.

According to the parents’ statement, as the ski patrol attempted to reach them by skiing down from above on the opposite side of the valley, an avalanche occurred that engulfed them and led to the death of their son.

Rescuers reportedly retrieved Max’s body some 20 minutes later but he could not be revived.

“It has been confirmed to us by the coroner that Max’s death was instant and painless,” his parents said in the statement.

The 16-year-old was a student at Sydney’s International Grammar school, which has offered support to his family and fellow students.

His parents on Monday thanked the school community, as well as family and friends, for their messages of love and support during what has been a “profoundly difficult time”.

“We can find no words to express how much and how deeply Max was loved by us, and by so many others,” they said.

St Anton police are investigating the incident and will prepare a final report.

“We respect and will not interfere with this process, but have in the meantime been given permission by them to issue this statement,” Thomas Meyer and Julie Schatz said.

Bergrettung St Anton, the local mountain rescue group, said it could not comment on the incident: “We don’t give information. Only the police will do that.”

More than two dozen people have been killed in weather-related accidents across Europe over the past few weeks.