The attack on Sunday was Australia's worst mass shooting in nearly 30 years, and is being investigated as an act of terrorism targeting the Jewish community.
The death toll stands at 16, including one of the gunmen, identified by police as 50-year old Sajid Akram, who was shot by police.
The man's 24-year-old son and alleged accomplice, Naveed Akram, was in critical condition in hospital after also being shot.
"The family members have expressed no knowledge of his radical mindset or activities, nor of the circumstances that led to his radicalisation," Telangana state police said in a statement.
Hyderabad is the capital of Telangana state.
Australian police said both men had travelled to the Philippines in November, the father on an Indian passport and the son was on an Australian one.
The purpose of the trip is under investigation, officials said, adding it was not conclusive they were linked to any terrorist group or whether they received training in that country.
Telangana police said the factors that led to the radicalisation of the two gunmen "appear to have no connection with India or any local influence in Telangana".
In its statement on Tuesday, Telangana police said Sajid Akram visited India on six occasions, mainly for family-related reasons, since he migrated to Australia in 1998.
There was no "adverse record" on him before he left India, the statement said.
