Victoria Police said they believed the woman’s husband, Ashok Raj Varikuppala, fled overseas.
Varikuppala is believed to have arrived at his in-laws’ home in the southern Indian city of Hyderabad with the couple’s young son.
Once there, he reportedly confessed to Swetha’s parents that he had suffocated their daughter.
“I am sorry for what I did, Chaithanya (Swetha) is no more, I killed her,” he reportedly told them.
“It happened unintentionally, I didn’t want to kill her. We had an argument, so I held her mouth and nose by my hand, and she suffocated to death.”
He reportedly claimed he wanted to return to Australia and surrender.
He reportedly then handed over their four-year-old son and left.
It’s understood the woman’s sister alerted Australian police from India, leading to the discovery of Swetha’s body on the side of a road.
Detectives believe Varikuppala is still in India but no formal extradition request has been submitted.
No arrests have been made.
If the 38-year-old flies back to Australia, he will be detained on arrival.
Victoria Police are remaining tight lipped on the process of the investigation.
“Due to the seriousness of the matter, there is much we unfortunately cannot comment on as we don’t want to jeopardise the ongoing investigation,” they said in a statement.
“This includes information about any ongoing enquiries or liaison with any other agencies here in Australia or internationally, or any liaison with the victim’s family.”
Family and friends are raising money to take Swetha’s body to India for burial, but have told Nine News they’re still waiting for confirmation from a funeral director as to whether she can be repatriated.
