The 38-year-old is wanted by Queensland detectives as the main suspect in the murder of Cordingley at Wanghetti Beach, north of Cairns, in 2018.
Cordingley’s body was found by her father Troy during a search of the sand dunes after she went missing.
The Indian government has already provisionally consented to Singh’s extradition, but the request must be signed off by the court.
“I want to go back. It is the (Indian) judicial system that has been holding things up,” Singh told AAP outside the Delhi court on Saturday.
“I did not kill the woman,” he said, adding he wanted to “reveal all the details” in an Australian court.
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Singh was arrested in Dehli in December ending a four-year manhunt for the 38-year-old.
His arrest came just weeks after the Queensland Government posted a $1 million reward for his capture.
The search for Singh began when he boarded a flight to India hours after Cordingley’s body was found in sand dunes.
He had worked as a nurse and lived in Innisfail with his wife and three children, but has been in India since 2018.