Their seven year old son was also with them but stayed behind the barrier while his parents rushed to help his brother.
It's not known if the boy lost consciousness because of the fumes or if the quicksand pulled him in.
Three family members visiting a steamy volcanic field near Naples have died after an 11-year-old boy entered an off-limits area and his parents followed to try to rescue him.
The family's 7-year-old son ran for helped and did not fall into the crater, The Guardian stated.
Firefighters said the family, which were from Turin, appeared to have died from asphyxia, possibly because of hot gases emanating from the ground.
A rescue crew with paramedics called to the scene shortly after midday was unable to save the trio.
The coffins of three dead people are carried away out of the volcanic zone. Source AAP
The Solfatara volcano is one of many volcanic craters in the Campi Flegrei area, 20 km (12 miles) west of Naples, which first opened up to tourists in 1900, according to its website. They have determined that the fields have risen by about 12in over a decade.
'I was at the Solfatara for work, along with other visitors we realised that something had happened and we approached the crater. A tragedy, they pulled out two bodies, then pulled us away.
"I express my closeness from the community of Pozzuoli to the family of the victims".
The Solfatara crater is a dormant volcano which still emits jets of steam filled with sulphurous fumes.
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